On the location of roots of graph polynomials

TL;DR

This paper investigates how the roots of various graph polynomials relate to the structural properties of the graphs they originate from, providing insights into the interplay between algebraic and combinatorial graph characteristics.

Contribution

It offers a comprehensive analysis of the relationship between the roots of key graph polynomials and graph properties, advancing understanding in algebraic graph theory.

Findings

Roots of graph polynomials reflect certain graph properties

Characterization of root locations for specific polynomials

Insights into how polynomial roots encode graph structure

Abstract

Roots of graph polynomials such as the characteristic polynomial, the chromatic polynomial, the matching polynomial, and many others are widely studied. In this paper we examine to what extent the location of these roots reflects the graph theoretic properties of the underlying graph.