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图的整数值控制函数

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Dominating functions with integer values in graphs——a survey
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) = Σv∈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.

P-dominating function, signed domination, signed total domination, minus domination, minus total domination.

康丽英、单而芳

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Department of Mathematics, College of Sciences, Shanghai University, Shanghai 200444, P. R. China

P-dominating function, signed domination, signed total domination, minus domination, minus total domination.

国家自然科学基金Shuguang Plan of Shanghai Education Development FoundationNatural Science Development Foundation of Shanghai Municipal Commission of Education

1057111706SG4205AZ04

2007

上海大学学报(英文版)
上海大学

上海大学学报(英文版)

影响因子：0.196
ISSN：1007-6417
年,卷(期)：2007.11(5)
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