We have the following:
From the graph of the question and the example, we can assume that the vertices remain the same, they only change for each corresponding letter, therefore:
vertex A of graph 1 corresponds to vertex V of graph 2
vertex B of graph 1 corresponds to vertex U of graph 2
vertex C of graph 1 corresponds to vertex X of graph 2
vertex D of graph 1 corresponds to vertex Z of graph 2
vertex E of graph 1 corresponds to vertex Y of graph 2
vertex F of graph 1 corresponds to vertex W of graph 2