Let G (V, E), H (V ', E ') be undirected graphs with f V V ' establishing an isomorphism between the graphs, (a) Prove that f 1 V V is also an isomorphism for G and H (b) If a V, prove that deg(a) (in G) deg(f(a)) (in H)

Question: Let G - (V, E), H = (V', E') be undirected graphs with f:V V' establishing an isomorphism between the graphs, (a) Prove that

Let G - (V, E), H = (V', E') be undirected graphs with f:V → V' establishing an isomorphism between the graphs,
(a) Prove that f-1 ; Vʹ → V is also an isomorphism for G and H.
(b) If a ∈ V, prove that deg(a) (in G) = deg(f(a)) (in H).

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