A conjecture on the diameter and signless Laplacian index of graphs

被引：7
作者：
Liu, Huiqing [1 ]
Lu, Mei [2 ]
机构：
[1] Hubei Univ, Sch Math & Comp Sci, Wuhan 430062, Peoples R China
[2] Tsinghua Univ, Dept Math Sci, Beijing 100084, Peoples R China
来源：
LINEAR ALGEBRA AND ITS APPLICATIONS | 2014年 / 450卷
关键词：
Graph; Signless Laplacian index; Diameter; SPECTRAL-RADIUS; BOUNDS; EIGENVALUE;
D O I：
10.1016/j.laa.2014.03.005
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
A bug Bug(p,q1,q2) is a graph obtained from a complete graph K-p by deleting an edge uv and attaching paths P-q1 and P-q2, at u and v, respectively. In this paper, we show that for connected graphs G of order n with signless Laplacian index q(1)(G) and diameter diam(G), q(1)(G) . diam(G) is maximized for and only for the graph Bug([n/2]+2,p,q), where p = [d/2], q = [d/2] and d = [(n+ 1)/2]. This solves a conjecture in [6] on the signless Laplacian index involving the diameter. (C) 2014 Elsevier Inc. All rights reserved.
引用
收藏
页码：158 / 174
页数：17
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