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

Title:

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

Creator:

Shi, Wei, Kang, Liying, and Wu, Suichao

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:fcef3296-8cd8-42aa-851a-8e05e804e10d
uuid:fcef3296-8cd8-42aa-851a-8e05e804e10d

Subject:

algebraic connectivity, Laplacian matrix, Laplacian spectral radius, signed domination, and total domination

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

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 $f\colon V(G)\rightarrow \{-1,1\}$ 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.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

315-325

Source:

Czechoslovak Mathematical Journal | 2010 Volume:60 | Number:2

Harvested from:

CDK

Metadata only:

false