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2009•Journal of Zhanjiang Normal CollegeRequires access

A Class of Graphs Whose Clique Transversal Numbers Equal Clique Independence Numbers

Erfang Shan

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Abstract

The clique-graph of a graph G,denoted K(G),is the graph obtained by taking the cliques of G as vertices,and two vertices are adjacent if and only if the corresponding cliques have nonempty intersection.In this paper,we prove that if the clique graph of G is a bipartite graph,then the clique transversal number of G equals the clique independence number of G.In addition,we present a polynomial-algorithm to decided whether the clique-graph of a graph G is a bipartite graph.

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What this paper is about

The clique-graph of a graph G,denoted K(G),is the graph obtained by taking the cliques of G as vertices,and two vertices are adjacent if and only if the corresponding cliques have nonempty intersection.In this paper,we prove that if the clique graph of G is a bipartite graph,then the clique transversal number of G equals the clique independence number of G.In addition,we present a polynomial-algorithm to decided whether the clique-graph of a graph G is a bipartite graph.

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Available abstract

The clique-graph of a graph G,denoted K(G),is the graph obtained by taking the cliques of G as vertices,and two vertices are adjacent if and only if the corresponding cliques have nonempty intersection.In this paper,we prove that if the clique graph of G is a bipartite graph,then the clique transversal number of G equals the clique independence number of G.In addition,we present a polynomial-algorithm to decided whether the clique-graph of a graph G is a bipartite graph.

Key concepts: Combinatorics, Simplex graph, Clique graph, Split graph, Mathematics, Block graph, Discrete mathematics, Independence number

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