Remarks on the minus (signed) total domination in graphs |
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Authors: | Erfang Shan T.C.E. Cheng |
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Affiliation: | a Department of Mathematics, Shanghai University, Shanghai 200444, China b Department of Logistics, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong |
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Abstract: | A function f:V(G)→{+1,0,-1} defined on the vertices of a graph G is a minus total dominating function if the sum of its function values over any open neighborhood is at least 1. The minus total domination number of G is the minimum weight of a minus total dominating function on G. By simply changing “{+1,0,-1}” in the above definition to “{+1,-1}”, we can define the signed total dominating function and the signed total domination number of G. In this paper we present a sharp lower bound on the signed total domination number for a k-partite graph, which results in a short proof of a result due to Kang et al. on the minus total domination number for a k-partite graph. We also give sharp lower bounds on and for triangle-free graphs and characterize the extremal graphs achieving these bounds. |
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Keywords: | 05C69 |
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