Title

On the A α spectral radius of digraphs with given parameters

Publication Date

1-1-2020

Document Type

Article

Department

Mathematics and Statistics

Publication Title

Linear and Multilinear Algebra

DOI

10.1080/03081087.2020.1793879

First Page

1

Last Page

16

Abstract

Let G be a digraph and (Formula presented.) be the adjacency matrix of G. Let (Formula presented.) be the diagonal matrix with outdegrees of vertices of G. For any real (Formula presented.), define the matrix (Formula presented.) as (Formula presented.) The largest modulus of the eigenvalues of (Formula presented.) is called the (Formula presented.) spectral radius of G. In this paper, we determine the digraphs which attain the maximum (or minimum) (Formula presented.) spectral radius among all strongly connected digraphs with given parameters such as girth, clique number, vertex connectivity or arc connectivity. We also propose an open problem.

Funding Number

2018JM1032

Funding Sponsor

National Natural Science Foundation of China

Keywords

adjacency matrix, parameters, signless Laplacian matrix, spectral radius, Strongly connected digraphs

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