图的整数值控制函数 |
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作者姓名: | 康丽英 单而芳 |
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作者单位: | Department of Mathematics, College of Sciences, Shanghai University, Shanghai 200444, P. R. China |
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基金项目: | Project supported by the National Natural Science Foundation of China (Grant No.10571117), the Shuguang Plan of Shang- hai Education Devel0pment Foundation (Grant No.06SG42), and the Natural Science Development Foundation of Shanghai Municipal Commission of Education (Grant No.05AZ04) |
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摘 要: | For an arbitrary subset P of the reals, a function f : V →P is defined to be a P-dominating function of a graph G = (V, E) if the sum of its function values over any closed neighbourhood is at least 1. That is, for every v ∈ V, f(N[v]) ≥ 1. The definition of total P-dominating function is obtained by simply changing ‘closed' neighborhood N[v] in the definition of P-dominating function to ‘open' neighborhood N(v). The (total) P-domination number of a graph G is defined to be the infimum of weight w(f) = ∑v ∈ V f(v) taken over all (total) P-dominating function f. Similarly, the P-edge and P-star dominating functions can be defined. In this paper we survey some recent progress on the topic of dominating functions in graph theory. Especially, we are interested in P-, P-edge and P-star dominating functions of graphs with integer values.
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关 键 词: | 图 整数值 控制函数 数学 |
收稿时间: | 2007-08-05 |
修稿时间: | 2007-08-02 |
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