Article Type

Research Article

Publication Title

AKCE International Journal of Graphs and Combinatorics

Abstract

In this article, we introduce a new matrix associated with a multidigraph, named as the complex adjacency matrix. We study the spectral properties of bipartite multidigraphs corresponding to the complex adjacency matrix. It is well known that a simple undirected graph is bipartite if and only if the spectrum of its adjacency matrix is symmetric about the origin (with multiplicity). We show that the result is not true in general for multidigraphs and supply a class of non-bipartite multidigraphs which have this property. We describe the complete spectrum of a multi-directed tree in terms of the spectrum of the corresponding modular tree. As a consequence, we get a class of Hermitian matrices for which the spectrum of a matrix in the class and the spectrum of the modulus (entrywise) of the matrix are the same.

First Page

466

Last Page

479

DOI

10.1016/j.akcej.2019.07.002

Publication Date

1-2-2020

Comments

Open Access, Gold

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