Consider the following three graphs:(i) Two of these graphs are isomorphic. Which? You must give a bijection and verify it is so, by using the method of adjacency matrices (see my class lecture of Thurs.. April 1). (ii) One of these graphs is not isomorphic to the others. Which one. and justify your answer. Solution the first and the last graphs are isomorphic while theirdegree sequences are (2,4,3,3,2,4) the order should be { a,b,c,d,e,f,g} and {f,m,p,q,o,n}isthe isomorphic graphs. by considering a relation h, we have h (a)= f, h(b) =m, h(c)= p, h(d) = q, h ( e) = 3, h(a)= name, h(f) = o this way, we can show that the first and last graphs areisomorphic. the middle graph has a different decreasing sequences. see that there is only one vertex with degree 2, where as thefirst and the last graphs have two 2 vertices graph..

1. Consider the following three graphs:(i) Two of these graphs are isomorphic. Which? You must
give a bijection and verify it is so, by using the method of adjacency matrices (see my class
lecture of Thurs.. April 1). (ii) One of these graphs is not isomorphic to the others. Which one.
and justify your answer.
Solution
the first and the last graphs are isomorphic while theirdegree sequences are (2,4,3,3,2,4)
the order should be { a,b,c,d,e,f,g} and {f,m,p,q,o,n}isthe isomorphic graphs.
by considering a relation h, we have h (a)= f, h(b) =m,
h(c)= p, h(d) = q, h ( e) = 3, h(a)= name, h(f) = o
this way, we can show that the first and last graphs areisomorphic.
the middle graph has a different decreasing sequences.
see that there is only one vertex with degree 2, where as thefirst and the last graphs have two 2
vertices graph.