I have identified two ways of showing it isomorphic but since it is a 9 mark question I dont think i have enough and neither has our teacher explained or given us enough notes on how it can be proven.
My answers so far below:
It is isomorphic as the Number of vertices on both graphs are 6 and the number of edges on both of the graphs are both 7.
Degree of nodes:
Deg (A) = 1 and Degree (T) = 1
Deg (B) = 3 and Degree (U) = 3
Deg (C) = 1 and Degree (Y) = 1
Deg (D) = 2 and Degree (V) = 2
Deg (E) = 1 and Degree (Z) = 1
Deg (F) = 3 and Degree (W) = 3
Deg (G) = 1 and Degree (X) = 1
Is the degree of nodes correct the way I have linked them?
Is what i have wrote above correct and enough or can more be explained? Please give solution to this question. Thanks.
Best Answer
Unfortunately, two non-isomorphic graphs can have the same degree sequence. See here for an example. Checking the degree sequence can only disprove that two graphs are isomorphic, but it can't prove that they are. In this case, I would just specify my isomorphism (which you've basically done, by identifying the vertices A and T, B and U, and so on) and then show that two vertices are connected by an edge in the original graph if and only if they are connected in the image. It's a little tedious, but should be something you can apply in general to these kinds of problems.