International Journal of Mathematics and Mathematical Sciences
Volume 12 (1989), Issue 1, Pages 77-84

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

Copyright © 1989 E. J. Farrell. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.