Upper minus total domination in small-degree regular graphs |
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Authors: | Hong Yan Xiaoqi Yang |
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Institution: | a Department of Logistics, The Hong Kong Polytechnic University, Hong Kong b Department of Applied Mathematics, The Hong Kong Polytechnic University, Hong Kong c Department of Mathematics, Shanghai University, Shanghai 200444, China |
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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 (MTDF) if the sum of its function values over any open neighborhood is at least one. An MTDF f is minimal if there does not exist an MTDF g:V(G)→{-1,0,1}, f≠g, for which g(v)?f(v) for every v∈V(G). The weight of an MTDF is the sum of its function values over all vertices. The minus total domination number of G is the minimum weight of an MTDF on G, while the upper minus domination number of G is the maximum weight of a minimal MTDF on G. In this paper we present upper bounds on the upper minus total domination number of a cubic graph and a 4-regular graph and characterize the regular graphs attaining these upper bounds. |
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Keywords: | 05C69 |
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