Bounds on Laplacian eigenvalues related to total and signed domination of graphs

被引：0
|
作者：
Wei Shi
Liying Kang
Suichao Wu
机构：
[1] Shanghai Sanda University,Department of Mathematics
[2] Shanghai University,School of Fundamentel Studies
[3] Shanghai University of Engineering Science,undefined
来源：
Czechoslovak Mathematical Journal | 2010年 / 60卷
关键词：
algebraic connectivity; Laplacian matrix; Laplacian spectral radius; signed domination; total domination; 05C50; 05C69;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
A total dominating set in a graph G is a subset X of V (G) such that each vertex of V (G) is adjacent to at least one vertex of X. The total domination number of G is the minimum cardinality of a total dominating set. A function f: V (G) → {−1, 1} is a signed dominating function (SDF) if the sum of its function values over any closed neighborhood is at least one. The weight of an SDF is the sum of its function values over all vertices. The signed domination number of G is the minimum weight of an SDF on G. In this paper we present several upper bounds on the algebraic connectivity of a connected graph in terms of the total domination and signed domination numbers of the graph. Also, we give lower bounds on the Laplacian spectral radius of a connected graph in terms of the signed domination number of the graph.
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页码：315 / 325
页数：10
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