POLYNOMIAL REPRESENTATIONS OF A BALANCED BICLIQUE COMMON NEIGHBORHOOD SYSTEM OF GRAPHS

Abstract

A biclique in a graph $G$ is a subset of $V(G)$ which induces a complete bipartite subgraph of $G$. It is said to be balanced if it has equivalent independent vertex partitions. In this paper, we introduce a graph polynomial which represents the number of balanced bicliques of $G$ of all possible orders with corresponding common neighborhood systems and establish some results on some special graphs. Received: September 25, 2023Revised: October 10, 2023Accepted: November 1, 2023