Clique Irreducibility and Clique Vertex Irreducibility of Graphs

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Clique Irreducibility and Clique Vertex Irreducibility of Graphs

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Title: Clique Irreducibility and Clique Vertex Irreducibility of Graphs
Author: Aparna, Lakshmanan S; Vijayakumar, A.
Abstract: A graphs G is clique irreducible if every clique in G of size at least two,has an edge which does not lie in any other clique of G and is clique reducible if it is not clique irreducible. A graph G is clique vertex irreducible if every clique in G has a vertex which does not lie in any other clique of G and clique vertex reducible if it is not clique vertex irreducible. The clique vertex irreducibility and clique irreducibility of graphs which are non-complete extended p-sums (NEPS) of two graphs are studied. We prove that if G(c) has at least two non-trivial components then G is clique vertex reducible and if it has at least three non-trivial components then G is clique reducible. The cographs and the distance hereditary graphs which are clique vertex irreducible and clique irreducible are also recursively characterized.
URI: http://dyuthi.cusat.ac.in/purl/2859
Date: 2009


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