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arXiv · 2206.12777

Hermitian adjacency matrices of mixed multigraphs

Bo-Jun Yuan·Shaowei Sun·Dijian Wang
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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.

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Bo-Jun Yuan, Shaowei Sun, Dijian Wang. 2022-06-26. Hermitian adjacency matrices of mixed multigraphs. https://arxiv.org/abs/2206.12777

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