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  3. 2 which of the following statements about graphs g and...

Question: 2 which of the following statements about graphs g and...

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2. Which of the following statements about graphs G and H are true? Substantiate your answers! (i) G and H are isomorphic if and only if for every map f: V(G) V(H) and for any two vertices u, v є V(G), we have {u,v} € (ii) G and H are isomorphic if and only if there exists a bijection (iii) If there exists a bijection f: V(G) -V(H) such that every ver- f E(G) E(H) tex u isomorphic V(G) has the same degree as f(u), then G and H are (iv) If G and H are isomorphic, then there exists a bijection f: V(G) - V (H) such that every vertex u E V(G) has the same degree as f(u) (v) If G and H are isomorphic, then there exists a bijection f E(G) E(H) (vi) G and H are isomorphic if and only if there exists a map f: V(G)V(H) such that for any two vertices u, v E V(G), we (vii) Every graph on n vertices is isomorphic to some graph on the (viii) Every graph onn 2 1 vertices is isomorphic to infinitely many vertex set {1,2,..., n] graphs.

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