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Locating and total dominating sets in trees
Discrete Applied Mathematics, 2006 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Haynes, Teresa W. +2 more
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(Total) Vector Domination for Graphs with Bounded Branchwidth
, 2013 Given a graph $G=(V,E)$ of order $n$ and an $n$-dimensional non-negative vector $d=(d(1),d(2),\ldots,d(n))$, called demand vector, the vector domination (resp., total vector domination) is the problem of finding a minimum $S\subseteq V$ such that every ...
B. Courcelle +26 more
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Hamiltonicity of 3tEC Graphs with α=κ+1
Journal of Mathematics, 2021 A set S of vertices in a graph G is a total dominating set of G if every vertex of G is adjacent to some vertex in S. The minimum cardinality of a total dominating set of G is the total domination number γtG of G.
Huanying He, Xinhui An, Zongjun Zhao
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Locating and Total Dominating Sets of Direct Products of Complete Graphs [PDF]
, 2011 A set S of vertices in a graph G = (V,E) is a metric-locating-total dominating set of G if every vertex of V is adjacent to a vertex in S and for every u ≠ v in V there is a vertex x in S such that d(u,x) ≠ d(v,x).
Iswadi, Hazrul
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Trees with unique minimum total dominating sets
Discussiones Mathematicae Graph Theory, 2002 A set \(S\) of vertices of a graph \(G\) is a total dominating set if every vertex of \(G\) is adjacent to some vertex in \(S\). Three equivalent conditions for a tree to have a unique minimum total dominating set together with a constructive characterization of such trees are given.
Haynes, Teresa W., Henning, Michael A.
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3-Tuple Total Domination Number of Rook’s Graphs
Discussiones Mathematicae Graph Theory, 2022 A k-tuple total dominating set (kTDS) of a graph G is a set S of vertices in which every vertex in G is adjacent to at least k vertices in S. The minimum size of a kTDS is called the k-tuple total dominating number and it is denoted by γ×k,t(G).
Pahlavsay Behnaz +2 more
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An Approximation Algorithm for a Variant of Dominating Set Problem
Axioms, 2023 In this paper, we consider a variant of dominating set problem, i.e., the total dominating set problem. Given an undirected graph G=(V,E), a subset of vertices T⊆V is called a total dominating set if every vertex in V is adjacent to at least one vertex ...
Limin Wang, Wenqi Wang
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On the total domatic number of regular graphs [PDF]
Transactions on Combinatorics, 2012 A set S of vertices of a graph G = (V;E) without isolated vertex is a total dominating set if every vertex of V (G) is adjacent to some vertex in S.
H. Aram +2 more
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An upper bound on the total outer-independent domination number of a tree [PDF]
Opuscula Mathematica, 2012 A total outer-independent dominating set of a graph \(G=(V(G),E(G))\) is a set \(D\) of vertices of \(G\) such that every vertex of \(G\) has a neighbor in \(D\), and the set \(V(G) \setminus D\) is independent.
Marcin Krzywkowski
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Bounding the Porous Exponential Domination Number of Apollonian Networks [PDF]
, 2014 Given a graph G with vertex set V, a subset S of V is a dominating set if every vertex in V is either in S or adjacent to some vertex in S. The size of a smallest dominating set is called the domination number of G.
Beverly, Joshua +3 more
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