International Journal of Mathematics and Mathematical Sciences 
Volume 12 (1989), Issue 1, Pages 77-84
doi:10.1155/S0161171289000104

On a class of polynomials associated with the Cliques in a graph and its applications

E. J. Farrell

 Department of Mathematics, The University of the West Indies, St. Augustine, Trinidad and Tobago
Received 24 November 1987; Revised 15 July 1988

Abstract

The clique polynomial of a graph is defined. An explicit formula is then derived for the clique polynomial of the complete graph. A fundamental theorem and a reduction process is then given for clique polynomials. Basic properties of the polynomial are also given. It is shown that the number theoretic functions defined by Menon are related to clique polynomials. This establishes a connection between the clique polynomial and decompositions of finite sets, symmetric groups and analysis.