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

Wei Shi; Liying Kang; Suichao Wu — 2010

Czechoslovak Mathematical Journal

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 $f : V (G) \to {- 1, 1}$ 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...

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