文献类型：期刊文献

英文题名：Spectral radius and edge-disjoint spanning trees

作者：Fan, Dandan[1,2];Gu, Xiaofeng[3];Lin, Huiqiu[1]

机构：[1]East China Univ Sci & Technol, Sch Math, Shanghai 200237, Peoples R China;[2]Xinjiang Agr Univ, Coll Math & Phys, Urumqi, Xinjiang, Peoples R China;[3]Univ West Georgia, Dept Comp & Math, Carrollton, GA USA

年份：2023

卷号：104

期号：4

起止页码：697

外文期刊名：JOURNAL OF GRAPH THEORY

收录：;EI(收录号：20232414250611);WOS:【SCI-EXPANDED(收录号:WOS:001003374400001)】；

基金：ACKNOWLEDGMENTS Dandan Fan was sponsored by Natural Science Foundation of Xinjiang Uygur Autonomous Region (No. 2022D01B103). Xiaofeng Gu was supported by a grant from the Simons Foundation (No. 522728), and Huiqiu Lin was supported by the National Natural Science Foundation of China (No. 12271162) and Natural Science Foundation of Shanghai (No. 22ZR1416300).

语种：英文

外文关键词：edge connectivity; eigenvalue; spanning tree packing; spectral radius

摘要：The spanning tree packing number of a graph G $G$, denoted by tau(G) $\tau (G)$, is the maximum number of edge-disjoint spanning trees contained in G $G$. The study of tau(G) $\tau (G)$ is one of the classic problems in graph theory. Cioaba and Wong initiated to investigate tau(G) $\tau (G)$ from spectral perspectives in 2012 and since then, tau(G) $\tau (G)$ has been well studied using the second-largest eigenvalue of the adjacency matrix in the past decade. In this paper, we further extend the results in terms of the number of edges and the spectral radius, respectively; and prove tight sufficient conditions to guarantee tau(G)>= k $\tau (G)\ge k$ with extremal graphs characterized. Moreover, we confirm a conjecture of Ning, Lu, and Wang on characterizing graphs with the maximum spectral radius among all graphs with a given order as well as fixed minimum degree and fixed edge connectivity. Our results have important applications in rigidity and nowhere-zero flows. We conclude with some open problems in the end.