Polynomials related to chromatic polynomials

TL;DR

This paper introduces new polynomials connected to the chromatic polynomial of a graph and explores their relationships, providing insights into graph coloring properties.

Contribution

It presents novel polynomials related to chromatic polynomials and investigates their interrelations, expanding understanding of graph coloring invariants.

Findings

New polynomials related to chromatic polynomials introduced

Relationships between these polynomials established

Potential applications in graph coloring theory discussed

Abstract

For a simple graph $G$, let $\chi(G,x)$ denote the chromatic polynomial of $G$. This manuscript introduces some polynomials which are related to chromatic polynomial and their relations.