唯一有效支配集

Isaac Reiter, Ju Zhou
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引用次数: 0

摘要

给定一个有限的简单图G,如果对于所有V∈V(G),V∈D或V与D中的某个顶点相邻,则集D⊆V(G)称为支配集。如果D中的顶点都不相邻,则支配集D是独立的,如果不在D中的每个顶点与D中恰好一个顶点相邻则D是完美的。如果支配集既独立又完美,则称之为有效支配集。对于图G,如果集D是G的唯一有效支配集,则称其为G的唯一高效支配集。本文提出了唯一有效支配集中的定义,探讨了具有唯一有效支配集合的图的性质,并完全刻画了具有唯一高效支配集合的几个图族。
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Unique Efficient Dominating Sets
Given a finite simple graph G, a set D ⊆ V(G) is called a dominating set if for all v ∈ V(G) , either v ∈ D or v is adjacent to some vertex in D. A dominating set D is independent if none of the vertices in D are adjacent, and D is perfect if each vertex not in D is adjacent to precisely one vertex in D. If a dominating set is both independent and perfect, then it is called an efficient dominating set. For a graph G, a set D is called a unique efficient dominating set of G if it is the only efficient dominating set of G. In this paper, the authors propose the definition of unique efficient dominating set, explore the properties of graphs with unique efficient dominating sets, and completely characterize several families of graphs which have unique efficient dominating sets.
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来源期刊
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