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Operations Research Transactions >

2024 , Vol. 28 >Issue 1: 121 - 130

DOI: https://doi.org/10.15960/j.cnki.issn.1007-6093.2024.01.010

On the eigenvalues and eigenvectors of Aα in weighted non-regular graphs

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  • 1. College of Science, University of Shanghai for Science and Technology, Shanghai 200093, China

Received date: 2020-09-02

  Online published: 2024-03-16

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, 2024, All rights reserved, without authorization
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Abstract

Let $G_\omega=(G, \omega)$ be a weighted graph, whose adjacency matrix and weighted degree diagnoal matrix are $A(G_\omega)$ and $D(G_\omega)$, respectively. For given $\alpha \in [0, 1]$, the matrix $A_\alpha(G_\omega)=\alpha D(G_\omega)+(1-\alpha)A(G_\omega)$ is the $A_\alpha$- matrix of $G_\omega$. In this paper, we give some bounds on the $A_\alpha$-eigenvalue of connected weighted non-regular graphs $G_\omega$, and obtain the lower bound of the ratio of the largest component to the smallest component in the eigenvector of the $A_\alpha$- spectral radius.

Key words： weighted graph; Aα-matrix; Aα-spectral radius

Cite this article

Changxiang HE, Wenyan WANG, Lele LIU . On the eigenvalues and eigenvectors of Aα in weighted non-regular graphs[J]. Operations Research Transactions, 2024 , 28(1) : 121 -130 . DOI: 10.15960/j.cnki.issn.1007-6093.2024.01.010

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