On the sum of the first two largest signless Laplacian eigenvalues of a graph

被引：2

作者：

Zhou, Zi-Ming ^{[1
]}

He, Chang-Xiang ^{[1
]}

Shan, Hai-Ying ^{[2
]}

机构：

[1] Univ Shanghai Sci & Technol, Coll Sci, Shanghai, Peoples R China

[2] Tongji Univ, Sch Math Sci, Shanghai, Peoples R China

来源：

DISCRETE MATHEMATICS | 2024年 / 347卷 / 09期

基金：

中国国家自然科学基金;

关键词：

(Signless) Laplacian matrix; (Signless) Laplacian eigenvalues; Sum of (signless) Laplacian eigenvalues;

D O I：

10.1016/j.disc.2024.114035

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

For a graph G, let S2(G) be the sum of the first two largest signless Laplacian eigenvalues of G, and f (G) = e(G) +3 -S2(G). Oliveira, Lima, Rama and Carvalho conjectured that K+1,n-1 (the star graph with an additional edge) is the unique graph with minimum value of f (G) on n vertices. In this paper, we prove this conjecture, which also confirm a conjecture for the upper bound of S2(G) proposed by Ashraf et al. (c) 2024 Elsevier B.V. All rights reserved.

引用

页数：14

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