On the Cospectrality of Hermitian Adjacency Matrices of Mixed Graphs

Authors

  • Omar Alomari German Jordanian University
  • Mohammad Abudayah German Jordanian University
  • Manal Ghanem The University of Jordan

DOI:

https://doi.org/10.29020/nybg.ejpam.v15i3.4422

Keywords:

Adjacency Matrix; Mixed graphs; Hermitian Matrix; Inverse Matrix; Spectrum; Bipartite graphs

Abstract

A mixed graph D is a graph that can be obtained from a graph by orienting some of its edges. Let α be a primitive n th root of unity, then the α−Hermitian adjacency matrix of a mixed graph is defined to be the matrix Hα = [hrs] where hrs = α if rs is an arc in D, hrs = α if sr is an arc in D, hrs = 1 if sr is a digon in D and hrs = 0 otherwise. In this paper we study the cospectrality of the Hermitian adjacency matrix of a mixed graph.

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Published

2022-07-31

Issue

Vol. 15 No. 3: (July 2022)

License

Copyright (c) 2022 European Journal of Pure and Applied Mathematics

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How to Cite

On the Cospectrality of Hermitian Adjacency Matrices of Mixed Graphs. (2022). European Journal of Pure and Applied Mathematics, 15(3), 1090-1097. https://doi.org/10.29020/nybg.ejpam.v15i3.4422