文章基本信息

标题：Algorithm to Find All Cliques in a Graph
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作者：A. Ashok Kumar ; S. Athisayanathan ; A. Antonysamy 等
期刊名称：International Journal of Advanced Networking and Applications
电子版ISSN：0975-0290
出版年度：2010
卷号：2
期号：2
页码：597-601
出版社：Eswar Publications
摘要：Let V = {1, 2, 3, . . . , n} be the vertex set of a graph G, P(V ) the powerset of V and A ¡ÊP(V ). Then A can be represented as an ordered n-tuple (x1x2x3. . .xn) where xi= 1 if i ¡ÊA, otherwise xi= 0 (1 ¡Ü i ¡Ü n). This representation is called binary count (or BC) representation of a set A and denoted as BC(A). Given a graph G of order n, it is shown that every integer m in S = {0, 1, 2, . . . , 2n- 1} corresponds to a subset A of V and vice versa. We introduce algorithms to find a subset A of the vertex set V = {1, 2, 3, . . . , n} of a graph G that corresponds to an integer m in S = {0, 1, 2, . . . , 2n- 1}, verify whether A is a subset of any other subset B of V and also verify whether the sub graph < A > induced b y the set A is a cliq ue or not using BC representation. Also a general algorithm to find all the cliques in a graph G using BC representation is introduced. Moreover we have proved the correctness of the algorithms and analyzed their time co mplexities
关键词：adjacency matrix; binary count; clique; powerset; subset