A survey on the matching polynomial

G Ivan - Graph Polynomials, 2016 - taylorfrancis.com
This chapter provides a preparation for the definition of the concept of a matching
polynomial. Here, we give some basic definitions and recall a few necessary facts from …

Matching measure, Benjamini–Schramm convergence and the monomer–dimer free energy

M Abért, P Csikvári, T Hubai - Journal of Statistical Physics, 2015 - Springer
We define the matching measure of a lattice L as the spectral measure of the tree of self-
avoiding walks in L. We connect this invariant to the monomer–dimer partition function of a …

Graphs with few matching roots

E Ghorbani - arxiv preprint arxiv:1011.0284, 2010 - arxiv.org
arxiv:1011.0284v3 [math.CO] 23 Apr 2012 Page 1 arxiv:1011.0284v3 [math.CO] 23 Apr
2012 Graphs with few matching roots Ebrahim Ghorbani Department of Mathematics, KN …

[HTML][HTML] Further results on the largest matching root of unicyclic graphs

W Liu, Q Guo, Y Zhang, L Feng, I Gutman - Discrete Applied Mathematics, 2017 - Elsevier
Let G be a simple connected graph with vertex set V (G). The matching polynomial of G is
defined as MG (x)=∑ k= 0 n∕ 2 (− 1) km (G, k) xn− 2 k, where m (G, k) denotes the number …

On the location of zeros of the Laplacian matching polynomials of graphs

JC Wan, Y Wang, A Mohammadian - Journal of Algebraic Combinatorics, 2022 - Springer
The Laplacian matching polynomial of a graph G, denoted by LM (G, x), is a new graph
polynomial whose all zeros are nonnegative real numbers. In this paper, we investigate the …

Maximum multiplicity of a root of the matching polynomial of a tree and minimum path cover

CY Ku, KB Wong - arxiv preprint arxiv:0810.4986, 2008 - arxiv.org
arxiv:0810.4986v1 [math.CO] 28 Oct 2008 Page 1 arxiv:0810.4986v1 [math.CO] 28 Oct 2008
Maximum Multiplicity of a Root of the Matching Polynomial of a Tree and Minimum Path Cover …

[HTML][HTML] Extensions of barrier sets to nonzero roots of the matching polynomial

CY Ku, KB Wong - Discrete Mathematics, 2010 - Elsevier
In matching theory, barrier sets (also known as Tutte sets) have been studied extensively
due to their connection to maximum matchings in a graph. For a root θ of the matching …

Distribution of zeros of matching polynomials of hypergraphs

JC Wan, Y Wang, Y Fan - arxiv preprint arxiv:2206.09558, 2022 - arxiv.org
Let $\h $ be a connected $ k $-graph with maximum degree ${\Delta}\geq 2$ and let $\mu
(\h, x) $ be the matching polynomial of $\h $. In this paper, we focus on studying the …

A refined Gallai-Edmonds structure theorem for weighted matching polynomials

TJ Spier - Discrete Mathematics, 2023 - Elsevier
In this work, we prove a refinement of the Gallai-Edmonds structure theorem for weighted
matching polynomials by Ku and Wong. Our proof uses a connection between matching …

The Ordering of the Unicyclic Graphs with respect to Largest Matching Root with Given Matching Number

L Gong, W Liu - Journal of Mathematics, 2022 - Wiley Online Library
The matching roots of a simple connected graph G are the roots of the matching polynomial
which is defined as MG x=∑ k= 0 n/2− 1 km G, kxn− 2 k, where m (G, k) is the number of the …