Please use this identifier to cite or link to this item: http://hdl.handle.net/10773/35242
Title: On the spectral radius of the generalized adjacency matrix of a digraph
Author: Baghipur, Maryam
Ganie, Hilal A.
Ghorbani, Modjtaba
Andrade, Enide
Keywords: Strongly connected digraph
Adjacency matrix
Aα-spectral radius
Maximum out-degree
Issue Date: 15-Nov-2022
Publisher: Elsevier
Abstract: Let $ D$ be a strongly connected digraph and $\alpha\in [0,1].$ In [J. P. Liu, X. Z. Wu, J. S. Chen and B. L. Liu, The $ A_{\alpha} $ spectral radius characterization of some digraphs, Linear Algebra Appl. 563 (2019) 63--74] the matrix $ A_{\alpha}(D)=\alpha Deg(D)+(1-\alpha)A(D),$ where $ A(D)$ and $Deg(D)$ are the adjacency matrix and the diagonal matrix of the out-degrees of $D,$ respectively, was defined. In this paper it is established some sharp bounds on the $A_{\alpha}(D)$-spectral radius in terms of some parameters such as the out-degrees, the maximum out-degree, the second maximum out-degree, the number of vertices, the number of arcs, the average $2$-outdegrees of the vertices of $D$ and the parameter $ \alpha$ of $A_{\alpha}(D)$. The extremal digraphs attaining these bounds are characterized. It is shown that the bounds obtained improve, in some cases, some of recently given bounds presented in the literature.
Peer review: yes
URI: http://hdl.handle.net/10773/35242
DOI: 10.1016/j.laa.2022.08.017
ISSN: 0024-3795
Publisher Version: https://www.sciencedirect.com/science/article/pii/S0024379522002944
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OGTCG - Artigos

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