How can I prove an "isomorphic equivalence" of a graph transformation?

Let F(G) be a graph transformation on G, e.g. the line graph transformation L(G). What is the best [general] approach for showing that $G_1 \isomorphic G_2 \iff F(G_1) \isomorphic F(G_2)$ ?

24 November 2015 9,990 4 View