Results 11 to 20 of about 46,459 (294)
$k$-Efficient partitions of graphs [PDF]
Communications in Combinatorics and Optimization, 2019 A set $S = \{u_1,u_2, \ldots, u_t\}$ of vertices of $G$ is an efficient dominating set if every vertex of $G$ is dominated exactly once by the vertices of $S$.
M. Chellali +2 more
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The Electronic Journal of Combinatorics, 2012 In this paper, we propose a new network reliability measure for some particular kind of service networks, which we refer to as domination reliability. We relate this new reliability measure to the domination polynomial of a graph and the coverage probability of a hypergraph.
Dohmen, Klaus, Tittmann, Peter
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Further Results on the Total Roman Domination in Graphs
Mathematics, 2020 Let G be a graph without isolated vertices. A function f : V ( G ) → { 0 , 1 , 2 } is a total Roman dominating function on G if every vertex v ∈ V ( G ) for which f ( v ) = 0 is adjacent to at least one vertex u ...
Abel Cabrera Martínez +2 more
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Relatively Prime Inverse Domination On Line Graph
Ratio Mathematica, 2023 Let G be non-trivial graph. A subset D of the vertex set V (G) of a graph G is called a dominating set of G if every vertex in V − D is adjacent to a vertex in D.
C. Jayasekaran, Roshini L
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AKCE International Journal of Graphs and Combinatorics, 2020 Let be a graph and let be a family of subsets of such that A dominating set of is called an -dominating set if for all The minimum cardinality of an -dominating of is called the -domination number of and is denoted by In this paper we present several ...
Manju Raju +3 more
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Graphs with equal domination and certified domination numbers [PDF]
Opuscula Mathematica, 2019 A set \(D\) of vertices of a graph \(G=(V_G,E_G)\) is a dominating set of \(G\) if every vertex in \(V_G-D\) is adjacent to at least one vertex in \(D\). The domination number (upper domination number, respectively) of \(G\), denoted by \(\gamma(G)\) (\(\
Magda Dettlaff +5 more
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HTS Teologiese Studies/Theological Studies, 2022 Violence has become a common phenomenon that affects women and children, particularly during the coronavirus disease 2019 (COVID-19) pandemic. While the lockdown regulations were meant to save lives by preventing further spread of the virus, another ...
Tshenolo J. Madigele, Gift T. Baloyi
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Hypo-efficient domination and hypo-unique domination
Communications in Combinatorics and Optimization, 2016 For a graph $G$ let $\gamma (G)$ be its domination number. We define a graph G to be (i) a hypo-efficient domination graph (or a hypo-$\mathcal{ED}$ graph) if $G$ has no efficient dominating set (EDS) but every graph formed by ...
V. Samodivkin
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Relating domination, exponential domination, and porous exponential domination
Discrete Optimization, 2017 The domination number $ (G)$ of a graph $G$, its exponential domination number $ _e(G)$, and its porous exponential domination number $ _e^*(G)$ satisfy $ _e^*(G)\leq _e(G)\leq (G)$. We contribute results about the gaps in these inequalities as well as the graphs for which some of the inequalities hold with equality.
Henning, Michael A. +2 more
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Dominating vertex covers: the vertex-edge domination problem [PDF]
Discussiones Mathematicae Graph Theory, 2021 A variant of domination, namely, vertex-edge domination in which a set of vertices dominating the edges is studied. The vertex-edge domination number of a graph \(G\), \(\gamma_{\mathrm{ve}}(G)\), is defined to be the cardinality of a smallest set \(D\) such that there exists a vertex cover \(C\) of \(G\) such that each vertex in \(C\) is dominated by ...
Klostermeyer, William F. +2 more
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