Graphs with few matching roots

TL;DR

This paper classifies graphs with at most five distinct zeros in their matching polynomial and identifies new graph families uniquely determined by this polynomial.

Contribution

It provides a complete characterization of graphs with limited matching polynomial roots and introduces new families uniquely identified by their matching polynomial.

Findings

Classified all graphs with ≤5 matching polynomial zeros

Identified new graph families determined by their matching polynomial

Enhanced understanding of the relationship between graph structure and matching polynomial roots

Abstract

We determine all graphs whose matching polynomials have at most five distinct zeros. As a consequence, we find new families of graphs which are determined by their matching polynomial.