Laplacian eigenvalues of the second power of a graph

被引：8
|
作者：
Das, Kinkar Ch. [1 ]
Guo, Ji-Ming [2 ]
机构：
[1] Sungkyunkwan Univ, Dept Math, Suwon 440746, South Korea
[2] China Univ Petr, Dept Appl Math, Dongying 257061, Shandong, Peoples R China
来源：
DISCRETE MATHEMATICS | 2013年 / 313卷 / 05期
关键词：
Graph; Laplacian matrix; Laplacian spectral radius; Second largest Laplacian eigenvalue; Diameter; PERFORMANCE GUARANTEES; SPECTRAL-RADIUS; NETWORKS; MATRICES; BOUNDS;
D O I：
10.1016/j.disc.2012.12.009
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
The kth power of a graph G, denoted by G(k), is the graph with the same vertex set as G, such that two vertices are adjacent in G(k) if and only if their distance is at most kin G. In this paper, we give bounds on the first two largest Laplacian eigenvalues of the second power of a general graph, and on the second power of a tree. We also give a Nordhaus-Gaddum-type inequality for the Laplacian spectral radius of G(2). (C) 2012 Elsevier B.V. All rights reserved.
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页码：626 / 634
页数：9
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