The construction of graphs with irreducible matching polynomials and their generalizations
Year: 2026
Type: article
Abstract: This paper investigates methods for constructing graphs whose matching polynomials are irreducible over Q. Building on this, the construction method is extended to general graph polynomials, for graphs whose polynomials satisfy certain properties, the connection construction produces a series of irreducible polynomial, such as characteristic polynomials and matching polynomials. Finally, the paper presents algorithms for calculating the matching polynomial of a given graph and the matching polynomial for a given number of vertices, implemented in Python.
Author: Hou Shengzhe
Institution: Jilin University of Chemical Technology
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $1,226
OpenAlex ID: W7120061792