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On the generalized adjacency spectral radius of digraphs
Linear and Multilinear Algebra ( IF 0.9 ) Pub Date : 2020-11-06 , DOI: 10.1080/03081087.2020.1844614
Hilal A. Ganie 1 , Maryam Baghipur 2
Affiliation  

ABSTRACT

Let D be a digraph of order n and let A(D) be the adjacency matrix of D. Let Deg(D) be the diagonal matrix of vertex out-degrees of D. For any real α[0,1], the generalized adjacency matrix Aα(D) of the digraph D is defined as Aα(D)=αDeg(D)+(1α)A(D). The largest modulus of the eigenvalues of Aα(D) is called the generalized adjacency spectral radius or the Aα-spectral radius of D. In this paper, we obtain some lower bounds for the spectral radius of Aα(D) in terms of the number of vertices, the number of arcs and the number of closed walks of the digraph D. The extremal graphs attained these lower bounds are determined. We also obtain some bounds for the spectral radius of Aα(D) in terms of the vertex out-degrees, the vertex average 2-out-degrees of the vertices of D and parameter α. We characterize the extremal digraphs attaining these bounds.



中文翻译:

关于有向图的广义邻接谱半径

摘要

Dn阶有向字母并令一个()D的邻接矩阵。让电子G()是D的顶点出度的对角矩阵。对于任何实α[0,1个], 广义邻接矩阵一个α()有向图D的定义为一个α()=α电子G()+(1个α)一个().的特征值的最大模数一个α()称为广义邻接谱半径或一个α-D的光谱半径。在本文中,我们获得了光谱半径的一些下界一个α()根据有向图D的顶点数、弧数和闭合步数。确定达到这些下限的极值图。我们还获得了光谱半径的一些界限一个α()在顶点出度方面,D和参数α的顶点的顶点平均2出度。我们描述了达到这些界限的极值有向图。

更新日期:2020-11-06
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