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Title: An application of the Turán theorem to domination in graphs
Authors: Shan, Erfang
Cheng, T. C. Edwin
Kang, Liying
Subjects: Turán theorem
Minus domination
Signed domination
Issue Date: 28-Jul-2008
Publisher: Elsevier B.V.
Source: Discrete applied mathematics, 28 July 2008, v. 156, no. 14, p. 2712–2718.
Abstract: A function f:V(G)→{+1,−1} defined on the vertices of a graph G is a signed dominating function if for any vertex v the sum of function values over its closed neighborhood is at least 1. The signed domination number γs(G) of G is the minimum weight of a signed dominating function on G. By simply changing “{+1,−1}” in the above definition to “{+1,0,−1}”, we can define the minus dominating function and the minus domination number of G. In this note, by applying the Turán theorem, we present sharp lower bounds on the signed domination number for a graph containing no (k+1)-cliques. As a result, we generalize a previous result due to Kang et al. on the minus domination number of k-partite graphs to graphs containing no (k+1)-cliques and characterize the extremal graphs.
Rights: Discrete Applied Mathematics © 2007 Elsevier B.V. The journal web site is located at
Type: Journal/Magazine Article
DOI: 10.1016/j.dam.2007.11.008
ISSN: 0166-218X
Appears in Collections:LMS Journal/Magazine Articles

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