The construction of graphs with irreducible matching polynomials and their generalizations
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.
Fields of Study & Subjects
Graph theory and applications
Polynomial and algebraic computation
Complexity and Algorithms in Graphs
Publication details
- Journal / source
- AKCE International Journal of Graphs and Combinatorics
- Pages
- 1–14
- Publication date
- 9 January 2026
- Language
- EN