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

@article{Shi2010,
abstract = {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\colon V(G)\rightarrow \lbrace -1,1\rbrace $ 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.},
author = {Shi, Wei, Kang, Liying, Wu, Suichao},
journal = {Czechoslovak Mathematical Journal},
keywords = {algebraic connectivity; Laplacian matrix; Laplacian spectral radius; signed domination; total domination; algebraic connectivity; Laplacian matrix; Laplacian spectral radius; signed domination; total domination},
language = {eng},
number = {2},
pages = {315-325},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Bounds on Laplacian eigenvalues related to total and signed domination of graphs},
url = {http://eudml.org/doc/38009},
volume = {60},
year = {2010},
}

TY - JOUR
AU - Shi, Wei
AU - Kang, Liying
AU - Wu, Suichao
TI - Bounds on Laplacian eigenvalues related to total and signed domination of graphs
JO - Czechoslovak Mathematical Journal
PY - 2010
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 60
IS - 2
SP - 315
EP - 325
AB - 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\colon V(G)\rightarrow \lbrace -1,1\rbrace $ 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.
LA - eng
KW - algebraic connectivity; Laplacian matrix; Laplacian spectral radius; signed domination; total domination; algebraic connectivity; Laplacian matrix; Laplacian spectral radius; signed domination; total domination
UR - http://eudml.org/doc/38009
ER -