Is it true that two graphs with eight vertices such that eac

Is it true that two graphs with eight vertices such that each vertex is incident with exactly three edges are isomorhic? Why or why not?

Solution

we know that

Two graph G and H are isomorphic if H can be obtained from G by relabeling the vertices - that is, if there is a one-to-one correspondence between the vertices of G and those of H, such that the number of edges joining any pair of vertices in G is equal to the number of edges joining the corresponding pair of vertices in H

and it is given that two graphs with eight vertices such that each vertex is incident with exactly three edges

so, there will be a one-to-one correspondence between the vertices of one graph with another graph, such that the number of edges joining any pair of vertices in first graph is equal to the number of edges joining the corresponding pair of vertices in second graph

Hence , these two graphs will be isomorphic...........Answer