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2. For n an integer, consider the set Vn of integers between 0 and n1, inclusive. (a) We regard two graphs as equal if they
2. For n an integer, consider the set Vn of integers between 0 and n1, inclusive. (a) We regard two graphs as equal if they contain the same vertices and the same edges. How many different graphs are there with vertex set Vn ? (b) We regard two graphs G1=(V1,E1) and G2=(V2,E2) as isomorphic if there exists a bijection f:V1V2 such that two vertices u,vV1 are connected by an edge in G1 if and only if f(u),f(v)V2 are connected by an edge in G2 (see section 10.3.5 in the textbook). Prove that if two graphs are equal, then they are isomorphic. (c) Draw two graphs G1,G2 both with vertex set V5 such that the graphs are not equal, but are isomorphic. Draw a third graph G3 with vertex set V5 which is not isomorphic to the G1 you've drawn. (d) How many distinct non-isomorphic graphs are there which have vertex set V3
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