Hermitian adjacency matrices of mixed multigraphs
Combinatorics
2022-06-28 v1
Abstract
A mixed multigraph is obtained from an undirected multigraph by orienting a subset of its edges. In this paper, we study a new Hermitian matrix representation of mixed multigraphs, give an introduction to cospectral operations on mixed multigraphs, and characterize switching equivalent mixed multigraphs in terms of fundamental cycle basis. As an application, an upper bound of cospectral classes of mixed multigraphs with the same underlying graph is obtained.
Cite
@article{arxiv.2206.12777,
title = {Hermitian adjacency matrices of mixed multigraphs},
author = {Bo-Jun Yuan and Shaowei Sun and Dijian Wang},
journal= {arXiv preprint arXiv:2206.12777},
year = {2022}
}
Comments
Mixed multigraph; Hermitian adjacency matrix; Switching equivalence; Cospectral class