On Clique Incidence Matrices and Derivatives of Clique Polynomials
Combinatorics
2022-05-18 v1
Abstract
The ordinary generating function of the number of complete subgraphs (cliques) of , denoted by , is called the The clique polynomial of the graph . In this paper, we first introduce some \emph{clique} incidence matrices associated by a simple graph as a generalization of the classical vertex-edge incidence matrix of . Then, using these clique incidence matrices, we obtain two clique-counting identities that can be used for deriving two combinatorial formulas for the first and the second derivatives of clique polynomials. Finally, we conclude the paper with several open questions and conjectures about possible extensions of our main results for higher derivatives of clique polynomials.
Keywords
Cite
@article{arxiv.2205.08133,
title = {On Clique Incidence Matrices and Derivatives of Clique Polynomials},
author = {Hossein Teimoori Faal},
journal= {arXiv preprint arXiv:2205.08133},
year = {2022}
}