On the Szeged and the Laplacian Szeged spectrum of a graph

被引：30
|
作者：
Fath-Tabar, Gholam Hossein [2 ]
Doslic, Tomislav [1 ]
Ashrafi, Ali Reza [2 ,3 ]
机构：
[1] Univ Zagreb, Fac Civil Engn, Zagreb 10000, Croatia
[2] Univ Kashan, Dept Math, Fac Sci, Kashan 8731751167, Iran
[3] Inst Res Fundamental Sci IPM, Sch Math, Tehran, Iran
来源：
LINEAR ALGEBRA AND ITS APPLICATIONS | 2010年 / 433卷 / 03期
关键词：
Szeged matrix; Laplacian matrix; Laplacian Szeged matrix; Szeged eigenvalue; Laplacian Szeged eigenvalue; Szeged index; VERTEX PI; INDEXES;
D O I：
10.1016/j.laa.2010.03.039
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
For a given graph G its Szeged weighting is defined by w(e) = n(u)(e)n(v)(e), where e = uv is an edge of G, n(u)(e) is the number of vertices of G closer to u than to v, and n(v)(e) is defined analogously. The adjacency matrix of a graph weighted in this way is called its Szeged matrix. In this paper we determine the spectra of Szeged matrices and their Laplacians for several families of graphs. We also present sharp upper and lower bounds on the eigenvalues of Szeged matrices of graphs. (C) 2010 Elsevier Inc. All rights reserved.
引用
收藏
页码：662 / 671
页数：10
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