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All Journal Electronic Journal of Graph Theory and Applications (EJGTA)
Hossein Teimoori Faal
Department of Mathematics and Computer Science, Allameh Tabataba’i University, Tehran, Iran
Electrical & Electronics Engineering

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Clique roots of K4-free chordal graphs Hossein Teimoori Faal
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 7, No 1 (2019): Electronic Journal of Graph Theory and Applications
Publisher : GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/ejgta.2019.7.1.8

Abstract

The clique polynomial C(G, x) of a finite, simple and undirected graph G = (V, E) is defined as the ordinary generating function of the number of complete subgraphs of G. A real root of C(G, x) is called a clique root of the graph G. Hajiabolhasan and Mehrabadi showed that every simple graph G has at least a clique root in the interval [ − 1, 0). Moreover, they showed that the class of triangle-free graphs has only clique roots. In this paper, we extend their result by showing that the class of K4-free chordal graphs has also only clique roots. In particular, we show that this class has always a clique root  − 1. We conclude our paper with some interesting open questions and conjectures.
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