Graph Domination in Distance Two
نویسندگان
چکیده
Let G = (V, E) be a graph, and k ≥ 1 an integer. A subgraph D is said to be k-dominating in G if every vertex of G−D is at distance at most k from some vertex of D. For a given class D of graphs, DomkD is the set of those graphs G in which every connected induced subgraph H has some k-dominating induced subgraph D ∈ D which is also connected. In our notation, DomD coincides with Dom1D. In this paper we prove that DomDomDu = Dom2Du holds for Du = {all connected graphs without induced Pu} (u ≥ 2). (In particular, D2 = {K1} and D3 = {all complete graphs}.) Some negative examples are also given.
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عنوان ژورنال:
- Discussiones Mathematicae Graph Theory
دوره 25 شماره
صفحات -
تاریخ انتشار 2005