A labeled graph G = (V, E) is a finite series of graph vertices V with a set of graph edges E of 2-subsets of V. Given a graph vertex set V_n = {1, 2, ..., n}, the number of vertex-labeled graphs is given by 2^(n(n - 1)/2). Two graphs G and H with graph vertices V_n = {1, 2, ..., n} are said to be isomorphic if there is a permutation p of V_n such that {u, v} is in the set of graph edges E(G) iff {p(u), p(v)} is in the set of graph edges E(H).

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