Locating–dominating sets in twin-free graphs
نویسندگان
چکیده
منابع مشابه
Locating-dominating sets in twin-free graphs
A locating-dominating set a of graph G is a dominating set D of G with the additional property that every two distinct vertices outside D have distinct neighbors in D; that is, for distinct vertices u and v outside D, N(u) ∩D 6= N(v) ∩D where N(u) denotes the open neighborhood of u. A graph is twin-free if every two distinct vertices have distinct open and closed neighborhoods. The location-dom...
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A total dominating set of a graph G is a set D of vertices of G such that every vertex of G has a neighbor in D. A locating-total dominating set of G is a total dominating set D of G with the additional property that every two distinct vertices outside D have distinct neighbors in D; that is, for distinct vertices u and v outside D, N(u) ∩D 6= N(v) ∩D where N(u) denotes the open neighborhood of...
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Let $D=(V,A)$ be a finite simple directed graph. A function$f:Vlongrightarrow {-1,0,1}$ is called a twin minus dominatingfunction (TMDF) if $f(N^-[v])ge 1$ and $f(N^+[v])ge 1$ for eachvertex $vin V$. The twin minus domination number of $D$ is$gamma_{-}^*(D)=min{w(f)mid f mbox{ is a TMDF of } D}$. Inthis paper, we initiate the study of twin minus domination numbersin digraphs and present some lo...
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Consider a connected undirected graph G = (V,E), a subset of vertices C ⊆ V , and an integer r ≥ 1; for any vertex v ∈ V , let Br(v) denote the ball of radius r centered at v, i.e., the set of all vertices linked to v by a path of at most r edges. If for all vertices v ∈ V , the sets Br(v) ∩C are all nonempty and different, then we call C an r-identifying code. A graph admits at least one r-ide...
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2016
ISSN: 0166-218X
DOI: 10.1016/j.dam.2015.06.038