A note on the lower bounds of signed domination number of a graph

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Abstract

Let G = (V,E) be a graph. For a function f:V →{-1,1], the weight of f is w(f) = Σv∈V f(v). For a vertex v in V', we define f[v] = Σu∈N[v] f(u). A signed dominating function of G is a function f : F-→{ -1,1} such that f[v]≥1 for all v ∈ V. The signed domination number γ s (G) of G is the minimum weight of a signed dominating function on G. A signed dominating function of a weight γ s (G) we call a γ s -function of G. In this paper, we study the signed domination problem of general graph, and obtain some lower bounds of the signed domination number of a graph, and show that these lower bounds are sharp, and extend a result in Dunbar et al. (1995). © 1999 Elsevier Science B.V. All rights reserved.

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Zhang, Z., Xu, B., Li, Y., & Liu, L. (1999). A note on the lower bounds of signed domination number of a graph. Discrete Mathematics, 195(1–3), 295–298. https://doi.org/10.1016/S0012-365X(98)00189-7

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