文献类型：期刊文献

英文题名：Spectral radius of graphs with given size and odd girth

作者：Lou, Zhenzhen[1];Lu, Lu[2];Huang, Xueyi[3]

机构：[1]Univ Shanghai Sci & Technol, Coll Sci, Shanghai 200093, Peoples R China;[2]Cent South Univ, Sch Math & Stat, Changsha 410083, Hunan, Peoples R China;[3]East China Univ Sci & Technol, Sch Math, Shanghai 200237, Peoples R China

年份：2024

卷号：31

期号：1

外文期刊名：ELECTRONIC JOURNAL OF COMBINATORICS

收录：;WOS:【SCI-EXPANDED(收录号:WOS:001184322300001)】；

基金：Acknowledgements The authors would like to express their gratitude to the anonymous referees for their invaluable suggestions that have significantly improved this paper. We are especially thankful to the referee who identified an error in the proof of Lemma 12 in the origi- nal version of the manuscript. Additionally, we extend our sincere appreciation to Dr. Yongtao Li for providing us with many valuable suggestions. This work is supported by NSFC (Nos. 12371362, 12061074, 12001544, 12171154, 11901540) and Natural Science Foundation of Hunan Province (No. 2021JJ40707) .

语种：英文

摘要：Let G(m,k) be the set of graphs with size m and odd girth (the length of shortest odd cycle) k. In this paper, we determine the graph maximizing the spectral radius among G(m,k) when m is odd. As byproducts, we show that, there is a number eta(m,k)>root m-k+3 such that every non bipartite graph G with size m and spectral radius rho >=eta(m,k) must contain an odd cycle of length less than k unless m is odd and G congruent to SKk,m, which is the graph obtained by subdividing an edge k(-2) times of the complete bipartite graph (K)2,m-k+2/(2). This result implies the main results of Zhai and Shu [Discrete Math. 345 (2022)] and settles a conjecture of Li and Peng [The Electronic J. Combin. 29 (4) (2022)] as well.