On Quipus whose signless Laplacian index does not exceed 4.5

被引：5

作者：

Belardo, Francesco ^{[1
]}

Brunetti, Maurizio ^{[1
]}

Trevisan, Vilmar ^{[1
,2
]}

Wang, Jianfeng ^{[3
]}

机构：

[1] Univ Naples Federico II, Dept Math & Applicat, Naples, Italy

[2] Univ Fed Rio Grande do Sul, Inst Matemat & Estat, BR-91509900 Porto Alegre, RS, Brazil

[3] Shandong Univ Technol, Sch Math & Stat, Zibo 255049, Peoples R China

来源：

JOURNAL OF ALGEBRAIC COMBINATORICS | 2022年 / 55卷 / 04期

基金：

中国国家自然科学基金;

关键词：

Hoffman-Smith limit point; Quipu; Spectral radius; Largest eigenvalue; SPECTRAL-RADIUS; GRAPHS;

D O I：

10.1007/s10801-021-01090-2

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Hoffman and Smith proved that in a graph with maximum degree Delta if all edges are subdivided infinitely many times, then the largest eigenvalue, also called index, of the adjacency matrix converges to Delta/(root Delta - 1). For the (signless) Laplacian of graphs, a similar result holds and the limit value is its square Delta(2)/(Delta - 1). Throughout the years, several scholars have progressed into characterizing the (connected) graphs whose adjacency or (signless) Laplacian index does not exceed the Hoffman-Smith limit value for Delta = 3, still there is not a complete characterization of such graphs. Here, we consider the signless Laplacian variant of this problem, and we characterize a large portion of such graphs. Also, we provide a structural restriction for the graphs not yet included for the complete characterization. Finally, we discuss the consequences on the adjacency variant of this problem.

引用

页码：1199 / 1223

页数：25

共 15 条

[11] Locating the eigenvalues of trees [J].