Linear separation of connected dominating sets in graphs
نویسندگان
چکیده
منابع مشابه
Linear Separation of Connected Dominating Sets in Graphs
A connected dominating set in a graph is a dominating set of vertices that induces a connected subgraph. We introduce and study the class of connected-domishold graphs, which are graphs that admit non-negative real weights associated to their vertices such that a set of vertices is a connected dominating set if and only if the sum of the corresponding weights exceeds a certain threshold. We sho...
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An odd dominating set of a simple, undirected graph G = (V,E) is a set of vertices D ⊆ V such that |N [v]∩D| ≡ 1 mod 2 for all vertices v ∈ V . It is known that every graph has an odd dominating set. In this paper we consider the concept of connected odd dominating sets. We prove that the problem of deciding if a graph has a connected odd dominating set is NP-complete. We also determine the exi...
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We propose algorithms for efficiently maintaining a constant-approximate minimum connected dominating set (MCDS) of a geometric graph under node insertions and deletions. Assuming that two nodes are adjacent in the graph iff they are within a fixed geometric distance, we show that an O(1)-approximate MCDS of a graph in R d with n nodes can be maintained with polylogarithmic (in n) work per node...
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Let G be a 2-connected graph. A subset D of V (G) is a 2-connected dominating set if every vertex of G has a neighbor in D and D induces a 2-connected subgraph. Let γ2(G) denote the minimum size of a 2-connected dominating set of G. Let δ(G) be the minimum degree of G. For an n-vertex graph G, we prove that γ2(G) ≤ n ln δ(G) δ(G) (1 + oδ(1)) where oδ(1) denotes a function that tends to 0 as δ →...
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A set S of vertices in a graph G=(V,E) is a dominating set ofG if every vertex of V-S is adjacent to some vertex of S.For an integer k≥1, a set S of vertices is a k-step dominating set if any vertex of $G$ is at distance k from somevertex of S. In this paper, using membership values of vertices and edges in fuzzy graphs, we introduce the concepts of strength of strongestdominating set as well a...
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ژورنال
عنوان ژورنال: Ars Mathematica Contemporanea
سال: 2019
ISSN: 1855-3974,1855-3966
DOI: 10.26493/1855-3974.1330.916