A Generalization of Clique Polynomials and Graph Homomorphism

Authors

  • Hossein Teimoori Faal Department of Mathematics and Computer Science, Allameh Tabatabai University, Tehran, Iran
  • Mortaza Bayat Department of Mathematics, Zanjan Branch Islamic Azad University, Zanjan, Iran

Keywords:

Weighted Clique Polynomial, Blow-Up Graph, No-Homomorphism Criteria

Abstract

The clique polynomial of a graph
G is the ordinary generating function of the number of
complete subgraphs (cliques) of $G$. In this paper, we introduce a new vertex-weighted version of these
polynomials. We also show that these weighted clique polynomials have always a real root
provided that the weights are non-negative real numbers. As an
application, we obtain a no-homomorphism criteria based on the largest real root
of our vertex-weighted clique polynomial.

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Published

2017-12-24

Issue

Vol. 12

Section

Vol. 12, No. 1, (2018)

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