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The Domination Parameters on a kind of the regular honeycomb structure [PDF]
Computer Science Journal of Moldova, 2022 The honeycomb mesh, based on hexagonal structure, has enormous applications in chemistry and engineering. A major challenge in this field is to understand the unique properties of honeycomb structures, which depend on their properties of topology. One
Fateme Movahedi +2 more
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Medium Domination Decomposition of Graphs
Ratio Mathematica, 2022 A set of vertices in a graph dominates if every vertex in is either in or adjacent to a vertex in . The size of any smallest dominating set is called domination number of .
E Ebin Raja Merly, Saranya J
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Stability of Domination in Graphs
Ratio Mathematica, 2023 The stability of dominating sets in Graphs is introduced and studied, in this paper. Here D is a dominating set of Graph G. In this paper the vertices of D and vertices of $V - D$ are called donors and acceptors respectively.
Reeja Kuriakose, K. S Parvathy
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A Note on the Paired-Domination Subdivision Number of Trees
Mathematics, 2021 For a graph G with no isolated vertex, let γpr(G) and sdγpr(G) denote the paired-domination and paired-domination subdivision numbers, respectively. In this note, we show that if T is a tree of order n≥4 different from a healthy spider (subdivided star),
Xiaoli Qiang +5 more
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Characterization of outerplanar graphs with equal 2-domination and domination numbers
Theory and Applications of Graphs, 2022 A {\em $k$-domination number} of a graph $G$ is minimum cardinality of a $k$-dominating set of $G$, where a subset $S \subseteq V(G)$ is a {\em $k$-dominating set} if each vertex $v\in V(G)\setminus S$ is adjacent to at least $k$ vertices in $S$.
Naoki Matsumoto
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On the Paired-Domination Subdivision Number of Trees
Mathematics, 2021 A paired-dominating set of a graph G without isolated vertices is a dominating set of vertices whose induced subgraph has perfect matching. The minimum cardinality of a paired-dominating set of G is called the paired-domination number γpr(G) of G.
Shouliu Wei +4 more
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On the edge geodetic and edge geodetic domination numbers of a graph [PDF]
Communications in Combinatorics and Optimization, 2020 In this paper, we study both concepts of geodetic dominating and edge geodetic dominating sets and derive some tight upper bounds on the edge geodetic and the edge geodetic domination numbers.
Vladimir Samodivkin
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On the out-domination and in-domination numbers of a digraph
Discrete Mathematics, 1999 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Gary Chartrand +2 more
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The paired-domination and the upper paired-domination numbers of graphs [PDF]
Opuscula Mathematica, 2015 In this paper we continue the study of paired-domination in graphs. A paired-dominating set, abbreviated PDS, of a graph \(G\) with no isolated vertex is a dominating set of vertices whose induced subgraph has a perfect matching.
Włodzimierz Ulatowski
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The Domination Number of Grids [PDF]
SIAM Journal on Discrete Mathematics, 2011 In this paper, we conclude the calculation of the domination number of all [Formula: see text] grid graphs. Indeed, we prove Chang’s conjecture saying that for every [Formula: see text], [Formula: see text].
Gonçalves, Daniel +3 more
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