Matching integral 2-connected graphs

TL;DR

This paper constructs an infinite family of 2-connected graphs with integer zeros in their matching polynomials, providing a negative answer to a previously posed question about the nature of these zeros.

Contribution

It introduces a new infinite family of 2-connected graphs whose matching polynomials have only integer zeros, countering earlier conjectures.

Findings

Established existence of infinite family with integer matching polynomial zeros

Counterexample to previous conjecture about zeros of matching polynomials

Advances understanding of the algebraic properties of graph polynomials

Abstract

In this note we present an infinite family of 2-connected graphs such that their matching polynomials have only integer zeros. This answers in negative a question of Akbari et al. [Graphs with integer matching polynomial zeros, Discrete Appl. Math. 224 (2017), 1-8].