SlideShare una empresa de Scribd logo

nossi ch 6

•Descargar como PPS, PDF•
•
L
lesaturner

power point for contemporary math ch 6

Tecnología
1 de 126
A Mathematical View of Our World 1 st ed. Parks, Musser, Trimpe, Maurer, and Maurer
Chapter 6 Routes and Networks
Section 6.1 Routing Problems ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
6.1 Initial Problem ,[object Object],[object Object]
Graphs ,[object Object],[object Object]
Graphs ,[object Object],[object Object],[object Object]
Equivalent Graphs ,[object Object]
Example 1 ,[object Object],A is connected to B, B to C, and C to D
Vertices and Edges ,[object Object],[object Object]
Example 2 ,[object Object],[object Object]
Example 2 ,[object Object],[object Object]
Example 3 ,[object Object],[object Object]
Example 3, cont’d ,[object Object],[object Object],[object Object],[object Object],[object Object]
Example 4 ,[object Object],[object Object],[object Object],[object Object]
Example 4, cont’d ,[object Object],[object Object],[object Object],[object Object]
Degree of a Vertex ,[object Object],[object Object],[object Object]
Example 5 ,[object Object]
Example 5 ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Example 5 ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Theorem ,[object Object],[object Object],[object Object]
Example 6 ,[object Object],[object Object]
Paths ,[object Object],[object Object],[object Object],[object Object]
Example 7 ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Circuits ,[object Object],[object Object]
Euler Paths ,[object Object],[object Object]
Euler Circuits ,[object Object],[object Object]
Connected Graphs ,[object Object],[object Object],[object Object]
Example 8 ,[object Object],[object Object]
Example 8, cont’d ,[object Object]
Example 9 ,[object Object],[object Object]
Example 10 ,[object Object],[object Object]
Degree Theorem ,[object Object],[object Object],[object Object],[object Object]
Euler’s Theorem ,[object Object],[object Object],[object Object]
Euler’s Theorem cont’d ,[object Object],[object Object],[object Object],[object Object],[object Object]
Euler’s Theorem cont’d ,[object Object],[object Object],[object Object],[object Object]
Example 11 ,[object Object],2 F 2 E 4 D 2 C 4 B 4 A Degree Vertex
Example 11 ,[object Object],[object Object]
Example 11, cont’d ,[object Object]
Fleury’s Algorithm ,[object Object],[object Object],[object Object],[object Object]
Fleury’s Algorithm, cont’d ,[object Object],[object Object],[object Object]
Fleury’s Algorithm, cont’d ,[object Object],[object Object]
Example 12 ,[object Object],[object Object]
6.1 Initial Problem Solution ,[object Object]
Initial Problem Solution, cont’d ,[object Object],[object Object]
Section 6.1 Assignment ,[object Object]
Section 6.2 Network Problems ,[object Object],[object Object],[object Object],[object Object],[object Object]
6.2 Initial Problem ,[object Object],[object Object],[object Object],[object Object]
Weighted Graphs ,[object Object]
Example 1 ,[object Object],[object Object],[object Object],[object Object],[object Object]
Example 1, cont’d ,[object Object],[object Object],[object Object],[object Object]
Example 1, cont’d ,[object Object]
Redundant Edges ,[object Object],[object Object],[object Object]
Subgraphs ,[object Object],[object Object]
Subgraphs ,[object Object]
Example 2 ,[object Object],[object Object],[object Object]
Example 2 ,[object Object]
Example 2 ,[object Object]
Example 2 ,[object Object]
Trees ,[object Object],[object Object],[object Object]
Trees, cont’d ,[object Object]
Example 3 ,[object Object],[object Object]
Example 3 ,[object Object]
Spanning Trees ,[object Object],[object Object],[object Object],[object Object]
Spanning Trees ,[object Object],[object Object]
Minimal Spanning Trees ,[object Object],[object Object]
Minimal Spanning Trees ,[object Object],[object Object],[object Object]
Kruskal’s Algorithm ,[object Object],[object Object]
Kruskal’s Algorithm ,[object Object],[object Object]
Kruskal’s Algorithm ,[object Object],[object Object]
Kruskal’s Algorithm ,[object Object],[object Object]
Kruskal’s Algorithm ,[object Object],[object Object]
Kruskal’s Algorithm ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Example 4 ,[object Object]
Example 4 ,[object Object],[object Object],[object Object]
Example 4 ,[object Object],[object Object],[object Object]
Example 4 ,[object Object],[object Object],[object Object]
Example 4 ,[object Object],[object Object],[object Object]
6.2 Initial Problem Solution ,[object Object]
Initial Problem Solution ,[object Object],[object Object]
Initial Problem Solution ,[object Object],[object Object]
Initial Problem Solution ,[object Object],[object Object]
Section 6.2 Assignment ,[object Object]
Section 6.3 Traveling-Salesperson Problem ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
6.3 Initial Problem ,[object Object],[object Object]
Hamiltonian Circuits ,[object Object],[object Object]
Example 1 ,[object Object],[object Object]
Example 2 ,[object Object],[object Object]
Hamiltonian Circuits, cont’d ,[object Object],[object Object]
Example 3 ,[object Object]
Example 3 ,[object Object],[object Object],[object Object]
Example 3, cont’d ,[object Object],[object Object]
Example 3, cont’d ,[object Object],[object Object],[object Object],[object Object]
Complete Graphs ,[object Object]
Example 4 ,[object Object]
Example 4, cont’d ,[object Object],[object Object]
Example 4, cont’d ,[object Object],[object Object]
Example 4, cont’d ,[object Object],[object Object]
Complete Graphs ,[object Object],[object Object],[object Object],[object Object]
Example 6 ,[object Object]
Example 6, cont’d ,[object Object]
Example 6, cont’d ,[object Object],[object Object],[object Object]
Theorem on Complete Graphs ,[object Object],[object Object],[object Object]
Question: ,[object Object],[object Object],[object Object],[object Object],[object Object]
Question: ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Traveling-Salesperson Problem ,[object Object],[object Object]
Complete Weighted Graphs ,[object Object],[object Object]
Question: ,[object Object],[object Object],[object Object],[object Object],[object Object]
Question: ,[object Object],[object Object],[object Object],[object Object],[object Object]
Example 7 ,[object Object],[object Object]
Example 7, cont’d ,[object Object],[object Object]
Example 7, cont’d
Example 7, cont’d ,[object Object],[object Object],[object Object]
Example 7, cont’d ,[object Object],[object Object]
Example 7, cont’d ,[object Object]
Example 7, cont’d ,[object Object],[object Object],[object Object],[object Object]
Traveling-Salesperson, cont’d ,[object Object],[object Object],[object Object],[object Object],[object Object]
Traveling-Salesperson, cont’d ,[object Object],[object Object],[object Object],[object Object],[object Object]
6.3 Initial Problem Solution ,[object Object]
Initial Problem Solution, cont’d ,[object Object],[object Object],[object Object]
Initial Problem Solution, cont’d ,[object Object],[object Object],[object Object]
Initial Problem Solution, cont’d ,[object Object],[object Object]
Initial Problem Solution, cont’d ,[object Object],[object Object]
Initial Problem Solution, cont’d ,[object Object],[object Object]
A fun website with Traveling Salesman Problem (TSP) Artwork: http://www.oberlin.edu/math/faculty/bosch/tspart-page.html
Section 6.3 Assignment ,[object Object]
Chapter 6 Assignments ,[object Object],[object Object],[object Object]

Recomendados

Graph: Euler path and Euler circuit
Graph: Euler path and Euler circuitGraph: Euler path and Euler circuit
Graph: Euler path and Euler circuitLiwayway Memije-Cruz
 
Graph theory 1
Graph theory 1Graph theory 1
Graph theory 1Tech_MX
 
Graph theory
Graph theoryGraph theory
Graph theoryTimothy Pastoral
 
Graph theory
Graph theoryGraph theory
Graph theorymanikanta361
 
Graph Theory
Graph TheoryGraph Theory
Graph TheoryEhsan Hamzei
 
Graphs-LeX2-given
Graphs-LeX2-givenGraphs-LeX2-given
Graphs-LeX2-givenAhmed M. H. Abdel-Fattah
 
Graph theory
Graph theoryGraph theory
Graph theoryAparnaKumari31
 
Graph data structure and algorithms
Graph data structure and algorithmsGraph data structure and algorithms
Graph data structure and algorithmsAnandhasilambarasan D
 

Recomendados

Graph: Euler path and Euler circuit
Graph: Euler path and Euler circuitGraph: Euler path and Euler circuit
Graph: Euler path and Euler circuitLiwayway Memije-Cruz
 
Graph theory 1
Graph theory 1Graph theory 1
Graph theory 1Tech_MX
 
Graph theory
Graph theoryGraph theory
Graph theoryTimothy Pastoral
 
Graph theory
Graph theoryGraph theory
Graph theorymanikanta361
 
Graph Theory
Graph TheoryGraph Theory
Graph TheoryEhsan Hamzei
 
Graphs-LeX2-given
Graphs-LeX2-givenGraphs-LeX2-given
Graphs-LeX2-givenAhmed M. H. Abdel-Fattah
 
Graph theory
Graph theoryGraph theory
Graph theoryAparnaKumari31
 
Graph data structure and algorithms
Graph data structure and algorithmsGraph data structure and algorithms
Graph data structure and algorithmsAnandhasilambarasan D
 
Applications of graphs
Applications of graphsApplications of graphs
Applications of graphsTech_MX
 
Graph theory introduction - Samy
Graph theory introduction - SamyGraph theory introduction - Samy
Graph theory introduction - SamyMark Arokiasamy
 
introduction to graph theory
introduction to graph theoryintroduction to graph theory
introduction to graph theoryChuckie Balbuena
 
d
dd
djagdeeparora86
 
Distruct week 15 graphs theory (updated)
Distruct week 15 graphs theory (updated)Distruct week 15 graphs theory (updated)
Distruct week 15 graphs theory (updated)Robert Almazan
 
Graphs and eularian circuit & path with c++ program
Graphs and eularian circuit & path with c++ programGraphs and eularian circuit & path with c++ program
Graphs and eularian circuit & path with c++ programMuhammad Danish Badar
 
A glimpse to topological graph theory
A glimpse to topological graph theoryA glimpse to topological graph theory
A glimpse to topological graph theoryANJU123MOHANAN
 
Slides Chapter10.1 10.2
Slides Chapter10.1 10.2Slides Chapter10.1 10.2
Slides Chapter10.1 10.2showslidedump
 
Graph
GraphGraph
GraphDaniel Rivera
 
Graph theory
Graph theoryGraph theory
Graph theoryNitesh Nayal
 
Graph theory
Graph theoryGraph theory
Graph theoryManash Kumar Mondal
 
Data structure - Graph
Data structure - GraphData structure - Graph
Data structure - GraphMadhu Bala
 
Graph algorithms
Graph algorithmsGraph algorithms
Graph algorithmsUniversity of Haripur
 
Graph Theory Introduction
Graph Theory IntroductionGraph Theory Introduction
Graph Theory IntroductionMANISH T I
 
Graph representation
Graph representationGraph representation
Graph representationTech_MX
 
Graphs-LeX12016
Graphs-LeX12016Graphs-LeX12016
Graphs-LeX12016Ahmed M. H. Abdel-Fattah
 
Graph theory and life
Graph theory and lifeGraph theory and life
Graph theory and lifeMilan Joshi
 
Graphs in data structure
Graphs in data structureGraphs in data structure
Graphs in data structurehamza javed
 
Matrix representation of graph
Matrix representation of graphMatrix representation of graph
Matrix representation of graphRounak Biswas
 
Adjacency list
Adjacency listAdjacency list
Adjacency listStefi Yu
 
Nossi Ch 4.1 and 4.2
Nossi Ch 4.1 and 4.2Nossi Ch 4.1 and 4.2
Nossi Ch 4.1 and 4.2lesaturner
 
Lesson 2.1 division
Lesson 2.1 divisionLesson 2.1 division
Lesson 2.1 divisionA V Prakasam
 

Más contenido relacionado

La actualidad más candente

Applications of graphs
Applications of graphsApplications of graphs
Applications of graphsTech_MX
 
Graph theory introduction - Samy
Graph theory introduction - SamyGraph theory introduction - Samy
Graph theory introduction - SamyMark Arokiasamy
 
introduction to graph theory
introduction to graph theoryintroduction to graph theory
introduction to graph theoryChuckie Balbuena
 
Distruct week 15 graphs theory (updated)
Distruct week 15 graphs theory (updated)Distruct week 15 graphs theory (updated)
Distruct week 15 graphs theory (updated)Robert Almazan
 
Graphs and eularian circuit & path with c++ program
Graphs and eularian circuit & path with c++ programGraphs and eularian circuit & path with c++ program
Graphs and eularian circuit & path with c++ programMuhammad Danish Badar
 
A glimpse to topological graph theory
A glimpse to topological graph theoryA glimpse to topological graph theory
A glimpse to topological graph theoryANJU123MOHANAN
 
Slides Chapter10.1 10.2
Slides Chapter10.1 10.2Slides Chapter10.1 10.2
Slides Chapter10.1 10.2showslidedump
 
Data structure - Graph
Data structure - GraphData structure - Graph
Data structure - GraphMadhu Bala
 
Graph Theory Introduction
Graph Theory IntroductionGraph Theory Introduction
Graph Theory IntroductionMANISH T I
 
Graph representation
Graph representationGraph representation
Graph representationTech_MX
 
Graph theory and life
Graph theory and lifeGraph theory and life
Graph theory and lifeMilan Joshi
 
Graphs in data structure
Graphs in data structureGraphs in data structure
Graphs in data structurehamza javed
 
Matrix representation of graph
Matrix representation of graphMatrix representation of graph
Matrix representation of graphRounak Biswas
 
Adjacency list
Adjacency listAdjacency list
Adjacency listStefi Yu
 

La actualidad más candente (20)

Applications of graphs
Applications of graphsApplications of graphs
Applications of graphs
 
Graph theory introduction - Samy
Graph theory introduction - SamyGraph theory introduction - Samy
Graph theory introduction - Samy
 
introduction to graph theory
introduction to graph theoryintroduction to graph theory
introduction to graph theory
 
d
dd
d
 
Distruct week 15 graphs theory (updated)
Distruct week 15 graphs theory (updated)Distruct week 15 graphs theory (updated)
Distruct week 15 graphs theory (updated)
 
Graphs and eularian circuit & path with c++ program
Graphs and eularian circuit & path with c++ programGraphs and eularian circuit & path with c++ program
Graphs and eularian circuit & path with c++ program
 
A glimpse to topological graph theory
A glimpse to topological graph theoryA glimpse to topological graph theory
A glimpse to topological graph theory
 
Slides Chapter10.1 10.2
Slides Chapter10.1 10.2Slides Chapter10.1 10.2
Slides Chapter10.1 10.2
 
Graph
GraphGraph
Graph
 
Graph theory
Graph theoryGraph theory
Graph theory
 
Graph theory
Graph theoryGraph theory
Graph theory
 
Data structure - Graph
Data structure - GraphData structure - Graph
Data structure - Graph
 
Graph algorithms
Graph algorithmsGraph algorithms
Graph algorithms
 
Graph Theory Introduction
Graph Theory IntroductionGraph Theory Introduction
Graph Theory Introduction
 
Graph representation
Graph representationGraph representation
Graph representation
 
Graphs-LeX12016
Graphs-LeX12016Graphs-LeX12016
Graphs-LeX12016
 
Graph theory and life
Graph theory and lifeGraph theory and life
Graph theory and life
 
Graphs in data structure
Graphs in data structureGraphs in data structure
Graphs in data structure
 
Matrix representation of graph
Matrix representation of graphMatrix representation of graph
Matrix representation of graph
 
Adjacency list
Adjacency listAdjacency list
Adjacency list
 

Destacado

Nossi Ch 4.1 and 4.2
Nossi Ch 4.1 and 4.2Nossi Ch 4.1 and 4.2
Nossi Ch 4.1 and 4.2lesaturner
 
Lesson 2.1 division
Lesson 2.1 divisionLesson 2.1 division
Lesson 2.1 divisionA V Prakasam
 
nossi ch 13 updated
nossi ch 13 updatednossi ch 13 updated
nossi ch 13 updatedlesaturner
 
ch 3 quiz follow-up
ch 3 quiz follow-upch 3 quiz follow-up
ch 3 quiz follow-uplesaturner
 
Nossi Ch 5 updated
Nossi Ch 5 updatedNossi Ch 5 updated
Nossi Ch 5 updatedlesaturner
 
1 5 Motor Control Theories
1 5 Motor Control Theories1 5 Motor Control Theories
1 5 Motor Control TheoriesAhmed Shawky
 
Boiler doc 05 basic control
Boiler doc 05 basic controlBoiler doc 05 basic control
Boiler doc 05 basic controlMars Tsani
 
5-6 Two-Digit Quotients
5-6 Two-Digit Quotients5-6 Two-Digit Quotients
5-6 Two-Digit QuotientsRudy Alfonso
 

Destacado (14)

Nossi Ch 4.1 and 4.2
Nossi Ch 4.1 and 4.2Nossi Ch 4.1 and 4.2
Nossi Ch 4.1 and 4.2
 
Lesson 2.1 division
Lesson 2.1 divisionLesson 2.1 division
Lesson 2.1 division
 
Nossi Ch 1
Nossi Ch 1Nossi Ch 1
Nossi Ch 1
 
Nossi ch 2
Nossi ch 2Nossi ch 2
Nossi ch 2
 
nossi ch 13 updated
nossi ch 13 updatednossi ch 13 updated
nossi ch 13 updated
 
ch 3 quiz follow-up
ch 3 quiz follow-upch 3 quiz follow-up
ch 3 quiz follow-up
 
Nossi ch 12
Nossi ch 12Nossi ch 12
Nossi ch 12
 
Nossi ch 3
Nossi ch 3Nossi ch 3
Nossi ch 3
 
Nossi Ch 5 updated
Nossi Ch 5 updatedNossi Ch 5 updated
Nossi Ch 5 updated
 
Nossi ch 10
Nossi ch 10Nossi ch 10
Nossi ch 10
 
1 5 Motor Control Theories
1 5 Motor Control Theories1 5 Motor Control Theories
1 5 Motor Control Theories
 
Boiler doc 05 basic control
Boiler doc 05 basic controlBoiler doc 05 basic control
Boiler doc 05 basic control
 
Basic Control Theory
Basic Control TheoryBasic Control Theory
Basic Control Theory
 
5-6 Two-Digit Quotients
5-6 Two-Digit Quotients5-6 Two-Digit Quotients
5-6 Two-Digit Quotients
 

Similar a nossi ch 6

distructweek15graphstheoryupdated-160227143444.pdf
distructweek15graphstheoryupdated-160227143444.pdfdistructweek15graphstheoryupdated-160227143444.pdf
distructweek15graphstheoryupdated-160227143444.pdfansariparveen06
 
Cs6702 graph theory and applications Anna University question paper apr may 2...
Cs6702 graph theory and applications Anna University question paper apr may 2...Cs6702 graph theory and applications Anna University question paper apr may 2...
Cs6702 graph theory and applications Anna University question paper apr may 2...appasami
 
Data structure graphs
Data structure graphsData structure graphs
Data structure graphsUma mohan
 
Graph ASS DBATU.pptx
Graph ASS DBATU.pptxGraph ASS DBATU.pptx
Graph ASS DBATU.pptxARVIND SARDAR
 
euler paths and circuit theorem.pptx
euler paths and circuit theorem.pptxeuler paths and circuit theorem.pptx
euler paths and circuit theorem.pptxMArunyNandinikkutty
 
ISOMORFISME, CONNECTIVITY EULER HAMILTON.pdf
ISOMORFISME, CONNECTIVITY EULER HAMILTON.pdfISOMORFISME, CONNECTIVITY EULER HAMILTON.pdf
ISOMORFISME, CONNECTIVITY EULER HAMILTON.pdfmurniatimurni9
 
Final Report
Final ReportFinal Report
Final ReportCan Liu
 
Graph theory ppt.pptx
Graph theory ppt.pptxGraph theory ppt.pptx
Graph theory ppt.pptxsaranyajey
 
Mithfh lecturenotes 9
Mithfh lecturenotes 9Mithfh lecturenotes 9
Mithfh lecturenotes 9Praveen Kumar
 
Eurler_Hamilton_Path_Circuit.pdf
Eurler_Hamilton_Path_Circuit.pdfEurler_Hamilton_Path_Circuit.pdf
Eurler_Hamilton_Path_Circuit.pdfRydaS1
 
Hamilton circuits7 19and22
Hamilton circuits7 19and22Hamilton circuits7 19and22
Hamilton circuits7 19and22shivam19942
 

Similar a nossi ch 6 (20)

ch10.5.pptx
ch10.5.pptxch10.5.pptx
ch10.5.pptx
 
distructweek15graphstheoryupdated-160227143444.pdf
distructweek15graphstheoryupdated-160227143444.pdfdistructweek15graphstheoryupdated-160227143444.pdf
distructweek15graphstheoryupdated-160227143444.pdf
 
Ds lec 5_chap4
Ds lec 5_chap4Ds lec 5_chap4
Ds lec 5_chap4
 
Graph ds
Graph dsGraph ds
Graph ds
 
Graph theory Eulerian graph
Graph theory Eulerian graphGraph theory Eulerian graph
Graph theory Eulerian graph
 
Cs6702 graph theory and applications Anna University question paper apr may 2...
Cs6702 graph theory and applications Anna University question paper apr may 2...Cs6702 graph theory and applications Anna University question paper apr may 2...
Cs6702 graph theory and applications Anna University question paper apr may 2...
 
Data structure graphs
Data structure graphsData structure graphs
Data structure graphs
 
Graph ASS DBATU.pptx
Graph ASS DBATU.pptxGraph ASS DBATU.pptx
Graph ASS DBATU.pptx
 
euler paths and circuit theorem.pptx
euler paths and circuit theorem.pptxeuler paths and circuit theorem.pptx
euler paths and circuit theorem.pptx
 
ISOMORFISME, CONNECTIVITY EULER HAMILTON.pdf
ISOMORFISME, CONNECTIVITY EULER HAMILTON.pdfISOMORFISME, CONNECTIVITY EULER HAMILTON.pdf
ISOMORFISME, CONNECTIVITY EULER HAMILTON.pdf
 
Final Report
Final ReportFinal Report
Final Report
 
graph ASS (1).ppt
graph ASS (1).pptgraph ASS (1).ppt
graph ASS (1).ppt
 
Graph theory ppt.pptx
Graph theory ppt.pptxGraph theory ppt.pptx
Graph theory ppt.pptx
 
Mithfh lecturenotes 9
Mithfh lecturenotes 9Mithfh lecturenotes 9
Mithfh lecturenotes 9
 
Eurler_Hamilton_Path_Circuit.pdf
Eurler_Hamilton_Path_Circuit.pdfEurler_Hamilton_Path_Circuit.pdf
Eurler_Hamilton_Path_Circuit.pdf
 
Graph algorithm
Graph algorithmGraph algorithm
Graph algorithm
 
INCIDENCE.pptx
INCIDENCE.pptxINCIDENCE.pptx
INCIDENCE.pptx
 
Hamilton circuits7 19and22
Hamilton circuits7 19and22Hamilton circuits7 19and22
Hamilton circuits7 19and22
 
7. Spanning trees
7. Spanning trees7. Spanning trees
7. Spanning trees
 
Magtibay buk bind#2
Magtibay buk bind#2Magtibay buk bind#2
Magtibay buk bind#2
 

Último

Automating Business Process via MuleSoft Composer | Bangalore MuleSoft Meetup...
Automating Business Process via MuleSoft Composer | Bangalore MuleSoft Meetup...Automating Business Process via MuleSoft Composer | Bangalore MuleSoft Meetup...
Automating Business Process via MuleSoft Composer | Bangalore MuleSoft Meetup...shyamraj55
 
FULL ENJOY 🔝 8264348440 🔝 Call Girls in Diplomatic Enclave | Delhi
FULL ENJOY 🔝 8264348440 🔝 Call Girls in Diplomatic Enclave | DelhiFULL ENJOY 🔝 8264348440 🔝 Call Girls in Diplomatic Enclave | Delhi
FULL ENJOY 🔝 8264348440 🔝 Call Girls in Diplomatic Enclave | Delhisoniya singh
 
The Codex of Business Writing Software for Real-World Solutions 2.pptx
The Codex of Business Writing Software for Real-World Solutions 2.pptxThe Codex of Business Writing Software for Real-World Solutions 2.pptx
The Codex of Business Writing Software for Real-World Solutions 2.pptxMalak Abu Hammad
 
Breaking the Kubernetes Kill Chain: Host Path Mount
Breaking the Kubernetes Kill Chain: Host Path MountBreaking the Kubernetes Kill Chain: Host Path Mount
Breaking the Kubernetes Kill Chain: Host Path MountPuma Security, LLC
 
Injustice - Developers Among Us (SciFiDevCon 2024)
Injustice - Developers Among Us (SciFiDevCon 2024)Injustice - Developers Among Us (SciFiDevCon 2024)
Injustice - Developers Among Us (SciFiDevCon 2024)Allon Mureinik
 
Enhancing Worker Digital Experience: A Hands-on Workshop for Partners
Enhancing Worker Digital Experience: A Hands-on Workshop for PartnersEnhancing Worker Digital Experience: A Hands-on Workshop for Partners
Enhancing Worker Digital Experience: A Hands-on Workshop for PartnersThousandEyes
 
08448380779 Call Girls In Diplomatic Enclave Women Seeking Men
08448380779 Call Girls In Diplomatic Enclave Women Seeking Men08448380779 Call Girls In Diplomatic Enclave Women Seeking Men
08448380779 Call Girls In Diplomatic Enclave Women Seeking MenDelhi Call girls
 
Pigging Solutions Piggable Sweeping Elbows
Pigging Solutions Piggable Sweeping ElbowsPigging Solutions Piggable Sweeping Elbows
Pigging Solutions Piggable Sweeping ElbowsPigging Solutions
 
Presentation on how to chat with PDF using ChatGPT code interpreter
Presentation on how to chat with PDF using ChatGPT code interpreterPresentation on how to chat with PDF using ChatGPT code interpreter
Presentation on how to chat with PDF using ChatGPT code interpreternaman860154
 
Install Stable Diffusion in windows machine
Install Stable Diffusion in windows machineInstall Stable Diffusion in windows machine
Install Stable Diffusion in windows machinePadma Pradeep
 
[2024]Digital Global Overview Report 2024 Meltwater.pdf
[2024]Digital Global Overview Report 2024 Meltwater.pdf[2024]Digital Global Overview Report 2024 Meltwater.pdf
[2024]Digital Global Overview Report 2024 Meltwater.pdfhans926745
 
Benefits Of Flutter Compared To Other Frameworks
Benefits Of Flutter Compared To Other FrameworksBenefits Of Flutter Compared To Other Frameworks
Benefits Of Flutter Compared To Other FrameworksSoftradix Technologies
 
Beyond Boundaries: Leveraging No-Code Solutions for Industry Innovation
Beyond Boundaries: Leveraging No-Code Solutions for Industry InnovationBeyond Boundaries: Leveraging No-Code Solutions for Industry Innovation
Beyond Boundaries: Leveraging No-Code Solutions for Industry InnovationSafe Software
 
#StandardsGoals for 2024: What’s new for BISAC - Tech Forum 2024
#StandardsGoals for 2024: What’s new for BISAC - Tech Forum 2024#StandardsGoals for 2024: What’s new for BISAC - Tech Forum 2024
#StandardsGoals for 2024: What’s new for BISAC - Tech Forum 2024BookNet Canada
 
Transforming Data Streams with Kafka Connect: An Introduction to Single Messa...
Transforming Data Streams with Kafka Connect: An Introduction to Single Messa...Transforming Data Streams with Kafka Connect: An Introduction to Single Messa...
Transforming Data Streams with Kafka Connect: An Introduction to Single Messa...HostedbyConfluent
 
A Domino Admins Adventures (Engage 2024)
A Domino Admins Adventures (Engage 2024)A Domino Admins Adventures (Engage 2024)
A Domino Admins Adventures (Engage 2024)Gabriella Davis
 
Kotlin Multiplatform & Compose Multiplatform - Starter kit for pragmatics
Kotlin Multiplatform & Compose Multiplatform - Starter kit for pragmaticsKotlin Multiplatform & Compose Multiplatform - Starter kit for pragmatics
Kotlin Multiplatform & Compose Multiplatform - Starter kit for pragmaticscarlostorres15106
 
04-2024-HHUG-Sales-and-Marketing-Alignment.pptx
04-2024-HHUG-Sales-and-Marketing-Alignment.pptx04-2024-HHUG-Sales-and-Marketing-Alignment.pptx
04-2024-HHUG-Sales-and-Marketing-Alignment.pptxHampshireHUG
 
Slack Application Development 101 Slides
Slack Application Development 101 SlidesSlack Application Development 101 Slides
Slack Application Development 101 Slidespraypatel2
 
SIEMENS: RAPUNZEL – A Tale About Knowledge Graph
SIEMENS: RAPUNZEL – A Tale About Knowledge GraphSIEMENS: RAPUNZEL – A Tale About Knowledge Graph
SIEMENS: RAPUNZEL – A Tale About Knowledge GraphNeo4j
 

Último (20)

Automating Business Process via MuleSoft Composer | Bangalore MuleSoft Meetup...
Automating Business Process via MuleSoft Composer | Bangalore MuleSoft Meetup...Automating Business Process via MuleSoft Composer | Bangalore MuleSoft Meetup...
Automating Business Process via MuleSoft Composer | Bangalore MuleSoft Meetup...
 
FULL ENJOY 🔝 8264348440 🔝 Call Girls in Diplomatic Enclave | Delhi
FULL ENJOY 🔝 8264348440 🔝 Call Girls in Diplomatic Enclave | DelhiFULL ENJOY 🔝 8264348440 🔝 Call Girls in Diplomatic Enclave | Delhi
FULL ENJOY 🔝 8264348440 🔝 Call Girls in Diplomatic Enclave | Delhi
 
The Codex of Business Writing Software for Real-World Solutions 2.pptx
The Codex of Business Writing Software for Real-World Solutions 2.pptxThe Codex of Business Writing Software for Real-World Solutions 2.pptx
The Codex of Business Writing Software for Real-World Solutions 2.pptx
 
Breaking the Kubernetes Kill Chain: Host Path Mount
Breaking the Kubernetes Kill Chain: Host Path MountBreaking the Kubernetes Kill Chain: Host Path Mount
Breaking the Kubernetes Kill Chain: Host Path Mount
 
Injustice - Developers Among Us (SciFiDevCon 2024)
Injustice - Developers Among Us (SciFiDevCon 2024)Injustice - Developers Among Us (SciFiDevCon 2024)
Injustice - Developers Among Us (SciFiDevCon 2024)
 
Enhancing Worker Digital Experience: A Hands-on Workshop for Partners
Enhancing Worker Digital Experience: A Hands-on Workshop for PartnersEnhancing Worker Digital Experience: A Hands-on Workshop for Partners
Enhancing Worker Digital Experience: A Hands-on Workshop for Partners
 
08448380779 Call Girls In Diplomatic Enclave Women Seeking Men
08448380779 Call Girls In Diplomatic Enclave Women Seeking Men08448380779 Call Girls In Diplomatic Enclave Women Seeking Men
08448380779 Call Girls In Diplomatic Enclave Women Seeking Men
 
Pigging Solutions Piggable Sweeping Elbows
Pigging Solutions Piggable Sweeping ElbowsPigging Solutions Piggable Sweeping Elbows
Pigging Solutions Piggable Sweeping Elbows
 
Presentation on how to chat with PDF using ChatGPT code interpreter
Presentation on how to chat with PDF using ChatGPT code interpreterPresentation on how to chat with PDF using ChatGPT code interpreter
Presentation on how to chat with PDF using ChatGPT code interpreter
 
Install Stable Diffusion in windows machine
Install Stable Diffusion in windows machineInstall Stable Diffusion in windows machine
Install Stable Diffusion in windows machine
 
[2024]Digital Global Overview Report 2024 Meltwater.pdf
[2024]Digital Global Overview Report 2024 Meltwater.pdf[2024]Digital Global Overview Report 2024 Meltwater.pdf
[2024]Digital Global Overview Report 2024 Meltwater.pdf
 
Benefits Of Flutter Compared To Other Frameworks
Benefits Of Flutter Compared To Other FrameworksBenefits Of Flutter Compared To Other Frameworks
Benefits Of Flutter Compared To Other Frameworks
 
Beyond Boundaries: Leveraging No-Code Solutions for Industry Innovation
Beyond Boundaries: Leveraging No-Code Solutions for Industry InnovationBeyond Boundaries: Leveraging No-Code Solutions for Industry Innovation
Beyond Boundaries: Leveraging No-Code Solutions for Industry Innovation
 
#StandardsGoals for 2024: What’s new for BISAC - Tech Forum 2024
#StandardsGoals for 2024: What’s new for BISAC - Tech Forum 2024#StandardsGoals for 2024: What’s new for BISAC - Tech Forum 2024
#StandardsGoals for 2024: What’s new for BISAC - Tech Forum 2024
 
Transforming Data Streams with Kafka Connect: An Introduction to Single Messa...
Transforming Data Streams with Kafka Connect: An Introduction to Single Messa...Transforming Data Streams with Kafka Connect: An Introduction to Single Messa...
Transforming Data Streams with Kafka Connect: An Introduction to Single Messa...
 
A Domino Admins Adventures (Engage 2024)
A Domino Admins Adventures (Engage 2024)A Domino Admins Adventures (Engage 2024)
A Domino Admins Adventures (Engage 2024)
 
Kotlin Multiplatform & Compose Multiplatform - Starter kit for pragmatics
Kotlin Multiplatform & Compose Multiplatform - Starter kit for pragmaticsKotlin Multiplatform & Compose Multiplatform - Starter kit for pragmatics
Kotlin Multiplatform & Compose Multiplatform - Starter kit for pragmatics
 
04-2024-HHUG-Sales-and-Marketing-Alignment.pptx
04-2024-HHUG-Sales-and-Marketing-Alignment.pptx04-2024-HHUG-Sales-and-Marketing-Alignment.pptx
04-2024-HHUG-Sales-and-Marketing-Alignment.pptx
 
Slack Application Development 101 Slides
Slack Application Development 101 SlidesSlack Application Development 101 Slides
Slack Application Development 101 Slides
 
SIEMENS: RAPUNZEL – A Tale About Knowledge Graph
SIEMENS: RAPUNZEL – A Tale About Knowledge GraphSIEMENS: RAPUNZEL – A Tale About Knowledge Graph
SIEMENS: RAPUNZEL – A Tale About Knowledge Graph
 

nossi ch 6

  • 1. A Mathematical View of Our World 1 st ed. Parks, Musser, Trimpe, Maurer, and Maurer
  • 2. Chapter 6 Routes and Networks
  • 3.
  • 4.
  • 5.
  • 6.
  • 7.
  • 8.
  • 9.
  • 10.
  • 11.
  • 12.
  • 13.
  • 14.
  • 15.
  • 16.
  • 17.
  • 18.
  • 19.
  • 20.
  • 21.
  • 22.
  • 23.
  • 24.
  • 25.
  • 26.
  • 27.
  • 28.
  • 29.
  • 30.
  • 31.
  • 32.
  • 33.
  • 34.
  • 35.
  • 36.
  • 37.
  • 38.
  • 39.
  • 40.
  • 41.
  • 42.
  • 43.
  • 44.
  • 45.
  • 46.
  • 47.
  • 48.
  • 49.
  • 50.
  • 51.
  • 52.
  • 53.
  • 54.
  • 55.
  • 56.
  • 57.
  • 58.
  • 59.
  • 60.
  • 61.
  • 62.
  • 63.
  • 64.
  • 65.
  • 66.
  • 67.
  • 68.
  • 69.
  • 70.
  • 71.
  • 72.
  • 73.
  • 74.
  • 75.
  • 76.
  • 77.
  • 78.
  • 79.
  • 80.
  • 81.
  • 82.
  • 83.
  • 84.
  • 85.
  • 86.
  • 87.
  • 88.
  • 89.
  • 90.
  • 91.
  • 92.
  • 93.
  • 94.
  • 95.
  • 96.
  • 97.
  • 98.
  • 99.
  • 100.
  • 101.
  • 102.
  • 103.
  • 104.
  • 105.
  • 106.
  • 107.
  • 108.
  • 109.
  • 110.
  • 112.
  • 113.
  • 114.
  • 115.
  • 116.
  • 117.
  • 118.
  • 119.
  • 120.
  • 121.
  • 122.
  • 123.
  • 124. A fun website with Traveling Salesman Problem (TSP) Artwork: http://www.oberlin.edu/math/faculty/bosch/tspart-page.html
  • 125.
  • 126.