Bounds on the locating-total domination number of a tree
نویسندگان
چکیده
منابع مشابه
Bounds on the differentiating-total domination number of a tree
Given a graphG = (V , E)with no isolated vertex, a subset S of V is called a total dominating set of G if every vertex in V is adjacent to a vertex in S. A total dominating set S is called a differentiating-total dominating set if for every pair of distinct vertices u and v in V , N[u] ∩ S ≠ N[v] ∩ S. The minimum cardinality of a differentiating-total dominating set of G is the differentiating-...
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Let $G$ be a graph with vertex set $V(G)$. For any integer $kge 1$, a signed (total) $k$-dominating functionis a function $f: V(G) rightarrow { -1, 1}$ satisfying $sum_{xin N[v]}f(x)ge k$ ($sum_{xin N(v)}f(x)ge k$)for every $vin V(G)$, where $N(v)$ is the neighborhood of $v$ and $N[v]=N(v)cup{v}$. The minimum of the values$sum_{vin V(G)}f(v)$, taken over all signed (total) $k$-dominating functi...
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A set S of vertices is a total dominating set of a graph G if every vertex of G is adjacent to some vertex in S. The minimum cardinality of a total dominating set is the total domination number t(G). We show that for a nontrivial tree T of order n and with ` leaves, t(T ) > (n+2 `)=2, and we characterize the trees attaining this lower bound. Keywords: total domination, trees. AMS subject classi...
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2011
ISSN: 0166-218X
DOI: 10.1016/j.dam.2010.12.025