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Weighted Domination of Independent Sets [PDF]
Graphs and Combinatorics, 2019 The {\em independent domination number} $ ^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 $ ^i$ is equal to $ $, the ordinary domination number.
Ron Aharoni, Irina Gorelik
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On the parameterized complexity of approximating dominating set [PDF]
Electron. Colloquium Comput. Complex., 2017 We study the parameterized complexity of approximating the k-Dominating Set (domset) problem where an integer k and a graph G on n vertices are given as input, and the goal is to find a dominating set of size at most F(k) · k whenever the graph G has a ...
S. KarthikC. +2 more
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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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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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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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Kernelization and Sparseness: the case of Dominating Set [PDF]
, 2015 We prove that for every positive integer $r$ and for every graph class $\mathcal G$ of bounded expansion, the $r$-Dominating Set problem admits a linear kernel on graphs from $\mathcal G$.
Drange, Pål Grønås +11 more
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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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Future Internet, 2019 A mobile ad-hoc network (MANET) is a temporary network of wireless mobile nodes. In a MANET, it is assumed that all of the nodes cooperate with each other to transfer data packets in a multi-hop fashion. However, some malicious nodes don’t cooperate with
Z. Zardari +6 more
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Super Dominating Sets in Graphs [PDF]
Proceedings of the National Academy of Sciences, India Section A: Physical Sciences, 2015 7 pages, 4 ...
Y. B. Venkatakrishnan +3 more
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Making a Dominating Set of a Graph Connected
Discussiones Mathematicae Graph Theory, 2018 Let G = (V,E) be a graph and S ⊆ V. We say that S is a dominating set of G, if each vertex in V \ S has a neighbor in S. Moreover, we say that S is a connected (respectively, 2-edge connected or 2-connected) dominating set of G if G[S] is connected ...
Li Hengzhe, Wu Baoyindureng, Yang Weihua
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