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In a Graph of $N$ Vertices, a subset of pairwise adjacent Vertices is known as a clique. A clique is a fully connected subgraph of a given graph. The problem of finding the size of a clique for a given Graph is an NP-Complete Problem. The number of graphs on $n$ nodes having 3 cliques are 0, 0, 1, 4, 12, 31, 67, ... (Sloane's A005289).

See also Clique Number, Maximum Clique Problem, Ramsey Number, Turán's Theorem


Sloane, N. J. A. Sequence A005289/M3440 in ``An On-Line Version of the Encyclopedia of Integer Sequences.'' and Sloane, N. J. A. and Plouffe, S. The Encyclopedia of Integer Sequences. San Diego: Academic Press, 1995.

© 1996-9 Eric W. Weisstein