Elsevier

Discrete Mathematics

Volume 195, Issues 1–3, 28 January 1999, Pages 295-298
Discrete Mathematics

Note
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) = ΣvV f(v). For a vertex v in V, we define f[v] = ΣuN[v] f(u). A signed dominating function of G is a function f : V → {−1, 1} such that f[v] ⩾ 1 for all vV. The signed domination number γs(G) of G is the minimum weight of a signed dominating function on G. A signed dominating function of a weight γs(G) we call a γs-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).

MSC

O5C15

Keywords

Graph
The signed dominating function
The signed domination number

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