Work

The \(\mathscr{G}\)-average of adjacency and Laplacian polynomials of a graph

Year: 2025

Type: article

Abstract: Let \(\mathscr{G}\) be a finite multiplicative group of quaternion unit \(U(\mathbb{H})\). The \(\mathscr{G}\)-average of adjacency (resp., Laplacian) polynomial of a graph \(G\) is defined as the arithmetic mean of the characteristic polynomials of adjacency (resp., Laplacian) matrice of all \(\mathscr{G}\)-gain graphs on \(G\). In this paper, we prove that the \(\mathscr{G}\)-average adjacency (resp., Laplacian) polynomial of a graph for any non-trivial finite subgroup \(\mathscr{G}\) of \(U(\mathbb{H})\) coincides with its matching (resp., weighted TU-subgraph) polynomial, which generalizes previous findings for signed graphs.

Source: American Journal of Combinatorics

DOI: 10.63151/amjc.v4i.28

Authors: Yaoping Hou, Wenjun Xie

Institution: Hunan Normal University

Language: English

Topic: Graph theory and applications

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funder: National Natural Science Foundation of China

Award: G478768364