New bounds on the signed domination numbers of graphs
نویسندگان
چکیده
A signed dominating function of a graph G with vertex set V is a function f : V → {−1, 1} such that for every vertex v in V the sum of the values of f at v and at every vertex u adjacent to v is at least 1. The weight of f is the sum of the values of f at every vertex of V . The signed domination number of G is the minimum weight of a signed dominating function of G. In this paper, we study the signed domination numbers of graphs and present new sharp lower and upper bounds for this parameter. As an example, we prove that the signed domination number of a tree of order n with leaves and s support vertices is at least (n+ 4 + 2( − s))/3. ∗ corresponding author S.M. HOSSEINI MOGHADDAM ET AL. /AUSTRALAS. J. COMBIN. 61 (3) (2015), 273–280 274
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ورودعنوان ژورنال:
- Australasian J. Combinatorics
دوره 61 شماره
صفحات -
تاریخ انتشار 2015