ArticleOriginal scientific text
Title
Clique irreducibility of some iterative classes of graphs
Authors 1, 1
Affiliations
- Department of Mathematics, Cochin University of Science and Technology, Cochin-682 022, India
Abstract
In this paper, two notions, the clique irreducibility and clique vertex irreducibility are discussed. A graph 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 it is clique vertex irreducible if every clique in G has a vertex which does not lie in any other clique of G. It is proved that L(G) is clique irreducible if and only if every triangle in G has a vertex of degree two. The conditions for the iterations of line graph, the Gallai graphs, the anti-Gallai graphs and its iterations to be clique irreducible and clique vertex irreducible are also obtained.
Keywords
line graphs, Gallai graphs, anti-Gallai graphs, clique irreducible graphs, clique vertex irreducible graphs
Bibliography
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Pages:
307-321
Main language of publication
English
Received
2007-10-09
Accepted
2008-03-18
Published
2008
DOI: 10.7151/dmgt.1407
Exact and natural sciences