Results 21 to 30 of about 53,392 (268)
The complexity of dominating set reconfiguration [PDF]
Theoretical Computer Science, 2015 Suppose that we are given two dominating sets $D_s$ and $D_t$ of a graph $G$ whose cardinalities are at most a given threshold $k$. Then, we are asked whether there exists a sequence of dominating sets of $G$ between $D_s$ and $D_t$ such that each dominating set in the sequence is of cardinality at most $k$ and can be obtained from the previous one by ...
Arash Haddadan +6 more
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On Two Open Problems on Double Vertex-Edge Domination in Graphs
Mathematics, 2019 A vertex v of a graph G = ( V , E ) , ve-dominates every edge incident to v, as well as every edge adjacent to these incident edges. A set S ⊆ V is a double vertex-edge dominating set if every edge of E is ve-dominated by at least two
Fang Miao +5 more
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On Relaxation of Dominant Sets
CoRR, 2022 In a graph $G = (V,E)$, a k-ruling set $S$ is one in which all vertices $V$ \ $S$ are at most $k$ distance from $S$. Finding a minimum k-ruling set is intrinsically linked to the minimum dominating set problem and maximal independent set problem, which have been extensively studied in graph theory.
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Hereditary Equality of Domination and Exponential Domination in Subcubic Graphs
Discussiones Mathematicae Graph Theory, 2021 Let γ(G) and γe(G) denote the domination number and exponential domination number of graph G, respectively. Henning et al., in [Hereditary equality of domination and exponential domination, Discuss. Math. Graph Theory 38 (2018) 275–285] gave a conjecture:
Chen Xue-Gang, Wang Yu-Feng, Wu Xiao-Fei
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Operations Research Letters, 2004 This paper presents several representation theorems for the solubility of three cost allocation problems, which are presented as cooperative games. In each problem, a graph \(G = (V, E)\) is given along with a cost function: given \(S \subseteq V\), \(c(S)\) is the cost of \(k\)-dominating the vertices in \(S\), i.e., building a set \(K \subseteq V ...
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Perfect Outer-connected Domination in the Join and Corona of Graphs
Recoletos Multidisciplinary Research Journal, 2016 Let 𝐺 be a connected simple graph. A dominating set 𝑆 ⊆ 𝑉(𝐺) is called a perfect dominating set of 𝐺 if each 𝑢 ∈ 𝑉 𝐺 ∖ 𝑆 is dominated by exactly one element of 𝑆.
Enrico Enriquez +3 more
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Mathematics, 2021 Many problems of practical interest can be modeled and solved by using fuzzy graph (FG) algorithms. In general, fuzzy graph theory has a wide range of application in various fields. Since indeterminate information is an essential real-life problem and is
Yongsheng Rao +4 more
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Minimum Neighborhood Domination of Split Graph of Graphs
مجلة بغداد للعلوم, 2023 Let be a non-trivial simple graph. A dominating set in a graph is a set of vertices such that every vertex not in the set is adjacent to at least one vertex in the set.
ANJALINE. W, A.STANIS ARUL MARY
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A Note on the Locating-Total Domination in Graphs
Discussiones Mathematicae Graph Theory, 2017 In this paper we obtain a sharp (improved) lower bound on the locating-total domination number of a graph, and show that the decision problem for the locating-total domination is NP-complete.
Miller Mirka +4 more
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Weighted Domination of Independent Sets [PDF]
Graphs and Combinatorics, 2019 The {\em independent domination number} $γ^i(G)$ of a graph $G$ is the maximum, over all independent sets $I$, of the minimal number of vertices needed to dominate $I$. It is known \cite{abz} that in chordal graphs $γ^i$ is equal to $γ$, the ordinary domination number.
Ron Aharoni, Irina Gorelik
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