Results 41 to 50 of about 7,293,468 (349)
On Resolvability- and Domination-Related Parameters of Complete Multipartite Graphs
Mathematics, 2022 Graphs of order n with fault-tolerant metric dimension n have recently been characterized.This paper points out an error in the proof of this characterization. We show that the complete multipartite graphs also have the fault-tolerant metric dimension n,
Sakander Hayat, Asad Khan, Yubin Zhong
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Independent sets with domination constraints [PDF]
Discrete Applied Mathematics, 1998 If \(\rho\) is a set of positive integers, then the \(\rho\)-IS problem is the problem to decide for a given graph \(G\), whether \(G\) has an independent set of vertices \(S\neq\varnothing\) with \(|S|\geq\min\{k\mid k\not\in\rho\}\) such that \(|N(v)\cap S|\in\rho\) for each \(v\in S\); here \(N(v)\) denotes the set of vertices adjacent to \(v\) in \(
Magnús M. Halldórsson +3 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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Dominating Sets in Projective Planes [PDF]
Journal of Combinatorial Designs, 2016 AbstractWe describe small dominating sets of the incidence graphs of finite projective planes by establishing a stability result that shows that dominating sets are strongly related to blocking and covering sets. Our main result states that if a dominating set in a projective plane of order is smaller than (i.e., twice the size of a Baer subplane ...
Héger, Tamás, Nagy, Zoltán Lóránt
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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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Journal of Graph Theory, 1994 AbstractLet G = (V, E) be a connected graph. A set D ⊂ V is a set‐dominating set (sd‐set) if for every set T ⊂ V − D, there exists a nonempty set S ⊂ D such that the subgraph 〈S ∪ T〉 induced by S ∪ T is connected. The set‐domination number γs(G) of G is the minimum cardinality of a sd‐set.
Sampathkumar, E., Latha, L. P.
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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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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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From Gap-ETH to FPT-Inapproximability: Clique, Dominating Set, and More [PDF]
IEEE Annual Symposium on Foundations of Computer Science, 2017 We consider questions that arise from the intersection between theareas of approximation algorithms, subexponential-time algorithms, and fixed-parameter tractable algorithms.
Parinya Chalermsook +6 more
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