Subdivision method in the Laplacian matching polynomial
Combinatorics
2024-10-21 v1
Abstract
As a bridge connecting the matching polynomial and the Laplacian matching polynomial of graphs, the subdivision method is expected to be useful for investigating the Laplacian matching polynomial. In this paper, we study applications of the method from three aspects. We prove that the zero sequence of the Laplacian matching polynomial of a graph majorizes its degree sequence, establishing a dual relation between the Laplacian matching polynomial and the characteristic polynomial of the signless Laplacian matrix of graphs. In addition, from different viewpoints, we give a new combinatorial interpretations for the coefficients of the Laplacian matching polynomial.
Keywords
Cite
@article{arxiv.2410.14112,
title = {Subdivision method in the Laplacian matching polynomial},
author = {Jiang-Chao Wan and Yi Wang and Zhi-Yuan Wang},
journal= {arXiv preprint arXiv:2410.14112},
year = {2024}
}