Open Access
April, 2023 The $A_{\alpha}$-spectral Radius of Bicyclic Graphs with Given Degree Sequences
Fei Wen, Mengyue Yuan, Wei Wang
Author Affiliations +
Taiwanese J. Math. 27(2): 207-220 (April, 2023). DOI: 10.11650/tjm/220906

Abstract

Let $A(G)$ and $D(G)$ be the adjacency matrix and the degree matrix of $G$, respectively. For any real $\alpha \in [0,1]$, Nikiforov defined the matrix $A_{\alpha}(G)$ as \[ A_{\alpha}(G) = \alpha D(G) + (1-\alpha) A(G). \] In this paper, we generalize some previous results about the $A_{1/2}$-spectral radius of bicyclic graphs with a given degree sequence. Furthermore, we characterize all extremal bicyclic graphs which have the largest $A_{\alpha}$-spectral radius in the set of all bicyclic graphs with prescribed degree sequences.

Funding Statement

This work is supported by National Natural Science Foundation of China (Grant Nos. 11961041, 12261055), Natural Science Foundation of Gansu Province, China (Grant No. 21JR11RA065) and Excellent Postgraduates of Gansu Provincial Department of Education “Star of Innovation” Foundation (No. 2021CXZX-594).

Acknowledgments

The authors would like to thank the referees for the valuable comments, and for the suggestions to improve the presented paper.

Citation

Download Citation

Fei Wen. Mengyue Yuan. Wei Wang. "The $A_{\alpha}$-spectral Radius of Bicyclic Graphs with Given Degree Sequences." Taiwanese J. Math. 27 (2) 207 - 220, April, 2023. https://doi.org/10.11650/tjm/220906

Information

Received: 11 November 2021; Revised: 3 July 2022; Accepted: 20 September 2022; Published: April, 2023
First available in Project Euclid: 3 October 2022

MathSciNet: MR4563516
zbMATH: 1515.05122
Digital Object Identifier: 10.11650/tjm/220906

Subjects:
Primary: 05C12 , 05C50

Keywords: $A_{\alpha}$-spectral radius , bicyclic graphs , degree sequence

Rights: Copyright © 2023 The Mathematical Society of the Republic of China

Vol.27 • No. 2 • April, 2023
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