Results 11 to 20 of about 5,038,045 (306)
CoRR, 2022 We consider a minimizing variant of the well-known \emph{No-Three-In-Line Problem}, the \emph{Geometric Dominating Set Problem}: What is the smallest number of points in an $n\times n$~grid such that every grid point lies on a common line with two of the points in the set?
Oswin Aichholzer +2 more
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Dominating Sets and Domination Polynomials of Paths [PDF]
International Journal of Mathematics and Mathematical Sciences, 2009 Let G = (V, E) be a simple graph. A set SβV is a dominating set of G, if every vertex in V\S is adjacent to at least one vertex in S. Let be the family of all dominating sets of a path Pn with cardinality i, and let . In this paper, we construct , and obtain a recursive formula for d(Pn, i).
Saeid Alikhani, Yee-Hock Peng
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New Algorithms for Mixed Dominating Set [PDF]
Discrete Mathematics & Theoretical Computer Science, 2021 A mixed dominating set is a collection of vertices and edges that dominates all vertices and edges of a graph. We study the complexity of exact and parameterized algorithms for \textsc{Mixed Dominating Set}, resolving some open questions.
Louis Dublois +2 more
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DOMINATION AND EDGE DOMINATION IN TREES
Ural Mathematical Journal, 2020 Let \(G=(V,E)\) be a simple graph. A set \(S\subseteq V\) is a dominating set if every vertex in \(V \setminus S\) is adjacent to a vertex in \(S\).
B. Senthilkumar +2 more
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New Results on Directed Edge Dominating Set [PDF]
Discrete Mathematics & Theoretical Computer Science, 2023 We study a family of generalizations of Edge Dominating Set on directed graphs called Directed $(p,q)$-Edge Dominating Set. In this problem an arc $(u,v)$ is said to dominate itself, as well as all arcs which are at distance at most $q$ from $v$, or at ...
RΓ©my Belmonte +4 more
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On redundant locating-dominating sets
Discrete Applied Mathematics, 2023 A locating-dominating set in a graph G is a subset of vertices representing "detectors" which can locate an "intruder" given that each detector covers its closed neighborhood and can distinguish its own location from its neighbors. We explore a fault-tolerant variant of locating-dominating sets called redundant locating-dominating sets, which can ...
Devin C. Jean, Suk Jai Seo
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Closed neutrosophic dominating set in neutrosophic graphs [PDF]
Neutrosophic Sets and Systems, 2023 The aim of this article is to concentrate on the notion of closed neutrosophic domination (CND) number πΎππ (πΊ) of a neutrosophic graph (NG) with using effective edge, furthermore we gain a few outcomes on this notion, the relation between πΎππ (πΊ) and ...
Amir Majeed Nabeel Arif
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On Hop Roman Domination in Trees [PDF]
Communications in Combinatorics and Optimization, 2019 Let $G=(V,E)$ be a graph. A subset $S\subset V$ is a hop dominating set if every vertex outside $S$ is at distance two from a vertex of $S$. A hop dominating set $S$ which induces a connected subgraph is called a connected hop dominating set of $G$.
N. Jafari Rad, A. Poureidi
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Connected End Anti-Fuzzy Equitable Dominating Set In Anti-Fuzzy Graphs
Ratio Mathematica, 2023 In this paper, the notion of connected end anti-fuzzy equitable dominating set of an anti-fuzzy graph is discussed. The connected end anti-fuzzy equitable domination number for some standard graphs are obtained.
Janofer K, S.Firthous Fatima
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Disjoint Secure Domination in the Join of Graphs
Recoletos Multidisciplinary Research Journal, 2016 Let G = (V(G),E(G)) be a simple connected graph. A dominating set S in G is called a secure dominating set in G if for every u β V (G) \ S, there exists v β S β© NG(u) such that (S \ {v}) βͺ {u} is a dominating set.
Jonecis Dayap, Enrico Enriquez
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