6-2) Prove that if two graphs G(V,R) and G′(V′,R′) are isomorphic and K = (x1, x2, …, xp) is a clique in G, then for any isomorphic mapping φ : V→V′, φ(K) = (φ(x1), φ(x2), …, φ(xp)) is a clique in G′.
6-3)
Prove that if two graphs G(V,R) and
G′(V′,R′) are isomorphic and
X⊂V, then for any isomorphic mapping φ :
V→V′, the subgraph H of G induced
on X is isomorphic to the subgraph H′ induced on
φ(x).