Question: 23. Let G and H be two graphs, where S is the set of vertices of degree r in G and T is the set

23. Let G and H be two graphs, where S is the set of vertices of degree r in G and T is the set of vertices of degree r in H (a) Prove that if G and H are isomorphic, then G[S] and H[T] are isomor phic (b) Give an example of two (non-isomorphic) graphs G and H having the same order and same size, where the degrees of the vertices of G are the same as the degrees of the vertices of H but where the statement in (a) is false for some r 23. Let G and H be two graphs, where S is the set of vertices of degree r in G and T is the set of vertices of degree r in H (a) Prove that if G and H are isomorphic, then G[S] and H[T] are isomor phic (b) Give an example of two (non-isomorphic) graphs G and H having the same order and same size, where the degrees of the vertices of G are the same as the degrees of the vertices of H but where the statement in (a) is false for some r

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