TITLE: Prove two graphs are isomorphic
QUESTION [18 upvotes]: 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.

REPLY [2 votes]: I find discrepancy in the first statement of your's - there are 7 vertices in both the graphs then you have 6 edges in both the graphs. This basic condition if true then it can further be proved that the two given simple graphs can be isomorphic or not? - depending onto the result. 
Next you made mappings from G(1st graph) to H(2nd graph)- which is correct but then also - you cannot say that these are isomorphic. What you need to do is - you need to make an adjacent matrix adj(G) and another adjacent matrix adj(h) where adj(h) will be as per the mappings you've done for the graph H using G!
if adj(G) and adj(h) are same, then you say that these graphs are isomorphic otherwise they aren't!
Hope you get it!