11 Determine which pairs of the general graphs in Figure 113

11. Determine which pairs of the general graphs in Figure 11.39 are isomorphic and, if isomorphic, find an isomorphism

Solution

I and III are isomorphic

Let first be named as ABCD from bottom left and third EFGH from bottom left

The mapping A to G, B to H, C to E and D to F is an isomorphism.

Since degree of A = degree of G, Deg of B = degree of H, ...

this isomorphism holds good.

II graph has no vertex of degree 4. Hence cannot be isomorphic to i or iii which has each one vertex of degree 4.

Iv graph has no vertex of degree 2, but all other 3 have vertices of degree 2. Hence iv is not isomorphic to any other 3.