Are the following pairs of graph isomorphic If so give an is

Are the following pairs of graph isomorphic? If so, give an isomorphism and justify why it is an isomorphism. If not, explain why (thoroughly).

Solution

If two graphs are isomorphic, they must have:

- the same number of vertices

- the same number of edges

- the same degrees for corresponding vertices

- the same number of connected components

- the same number of loops

- the same number of parallel edges.

Hence comparing in G1 & G2 :

No. of vertices, V1 = 7 And V2 = 7

No. of edges, E1 = 10 and E2 = 10

Degree of vertices, in G1 = 2,3,3,3,3,3,3 and in G2 = 2,3,3,3,3,3,3

No. of parallel Edges: in G1 = 0, in G2 = 0

No. of Loop: in G1 = 0, and in G2 = 0;

Hence the two graphs G1 and G2 are isomorphic