Results 51 to 60 of about 9,917,456 (366)
Isolate and independent domination number of some classes of graphs
AKCE International Journal of Graphs and Combinatorics, 2019 In this paper we compute isolate domination number and independent domination number of some well known classes of graphs. Also a counter example is provided, which disprove the result on independent domination for Euler Totient Cayley graph proved by ...
Shilpa T. Bhangale, Madhukar M. Pawar
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On the Total Outer k-Independent Domination Number of Graphs
Mathematics, 2020 A set of vertices of a graph G is a total dominating set if every vertex of G is adjacent to at least one vertex in such a set. We say that a total dominating set D is a total outer k-independent dominating set of G if the maximum degree of the subgraph ...
A. Cabrera-Martínez +3 more
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Reducing the domination number of graphs via edge contractions [PDF]
International Symposium on Mathematical Foundations of Computer Science, 2019 In this paper, we study the following problem: given a connected graph $G$, can we reduce the domination number of $G$ by at least one using $k$ edge contractions, for some fixed integer $k \geq 0$?
Esther Galby, Paloma T. Lima, B. Ries
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On graphs with equal domination and connected domination numbers
Discrete Mathematics, 1999 A subset \(S\) of the vertex set \(V(G)\) of a graph \(G\) is called dominating in \(G\), if each vertex of \(G\) either is in \(S\), or is adjacent to a vertex of \(S\). The minimum number of vertices of a dominating set in \(G\) is the dominating number \(\gamma(G)\) of \(G\).
Subramanian Arumugam, J. Paulraj Joseph
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Equitable eccentric domination in graphs
Ratio Mathematica, 2023 In this paper, we define equitable eccentric domination in graphs. An eccentric dominating set S ⊆ V (G) of a graph G(V, E) is called an equitable eccentric dominating set if for every v ∈ V − S there exist at least one vertex u ∈ V such that |d(v) − d(u)
A Riyaz Ur Rehman, A Mohamed Ismayil
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The 3-Rainbow Domination Number of the Cartesian Product of Cycles
Mathematics, 2020 We have studied the k-rainbow domination number of C n □ C m for k ≥ 4 (Gao et al. 2019), in which we present the 3-rainbow domination number of C n □ C m , which should be bounded above by the four-rainbow domination number of C n □ C m .
Hong Gao, Changqing Xi, Yuansheng Yang
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Domination cover number of graphs [PDF]
Discrete Mathematics, Algorithms and Applications, 2019 A set [Formula: see text] for the graph [Formula: see text] is called a dominating set if any vertex [Formula: see text] has at least one neighbor in [Formula: see text]. Fomin et al. [Combinatorial bounds via measure and conquer: Bounding minimal dominating sets and applications, ACM Transactions on Algorithms (TALG) 5(1) (2008) 9] gave an algorithm ...
M. Alambardar Meybodi +3 more
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Characterization of Upper Detour Monophonic Domination Number
Cubo, 2020 This paper introduces the concept of \textit{upper detour monophonic domination number} of a graph. For a connected graph $G$ with vertex set $V(G)$, a set $M\subseteq V(G)$ is called minimal detour monophonic dominating set, if no proper subset of $M ...
M. Mohammed Abdul Khayyoom
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All graphs with paired-domination number two less than their order [PDF]
Opuscula Mathematica, 2013 Let \(G=(V,E)\) be a graph with no isolated vertices. A set \(S\subseteq V\) is a paired-dominating set of \(G\) if every vertex not in \(S\) is adjacent with some vertex in \(S\) and the subgraph induced by \(S\) contains a perfect matching.
Włodzimierz Ulatowski
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A note on the bounds of Roman domination numbers
AIMS Mathematics, 2021 Let $G$ be a graph and $f: V(G) \rightarrow \{0,1,2\}$ be a mapping. $f$ is said to be a Roman dominating function of $G$ if every vertex $u$ for which $f(u) = 0$ is adjacent to at least one vertex $v$ for which $f(v)=2$.
Zepeng Li
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