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Connected domination critical graphs
Applied Mathematics Letters, 2004 A dominating set in a graph G is a connected dominating set of G if it induces a connected subgraph of G. The minimum number of vertices in a connected dominating set of G is called the connected domination number of G, and is denoted by γc(G).
Sun, Liang, Ma, De-Xiang, Chen, Xue-Gang
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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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The Connected Domination Number of Grids [PDF]
, 2021 Closed form expressions for the domination number of an $n \times m$ grid have attracted significant attention, and an exact expression has been obtained in 2011 by Gonçalves et al. In this paper, we present our results on obtaining new lower bounds on the connected domination number of an $n \times m$ grid.
Adarsh Srinivasan, N. S. Narayanaswamy
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Rainbow Connection Number and Connected Dominating Sets [PDF]
Electronic Notes in Discrete Mathematics, 2011 AbstractThe rainbow connection number of a connected graph is the minimum number of colors needed to color its edges, so that every pair of its vertices is connected by at least one path in which no two edges are colored the same. In this article we show that for every connected graph on n vertices with minimum degree δ, the rainbow connection number ...
L. Sunil Chandran +3 more
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Enumerating Connected Dominating Sets
CoRR, 2022 The question to enumerate all inclusion-minimal connected dominating sets in a graph of order $n$ in time significantly less than $2^n$ is an open question that was asked in many places. We answer this question affirmatively, by providing an enumeration algorithm that runs in time $\mathcal{O}(1.9896^n)$, using polynomial space only.
Faisal N. Abu-Khzam +4 more
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Bridge domination in fuzzy graphs [PDF]
Journal of Fuzzy Extension and Applications, 2023 In communication networks, strong connectivity between nodes is critical. The failure of strong connectivity between nodes may jeopardize the network’s stability. In fuzzy graphs, various dominating sets using strong edges are identified to avoid network
Sivasankar Shanmugam +2 more
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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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Connected Dominating Sets in Triangulations
CoRR, 2023 We show that every $n$-vertex triangulation has a connected dominating set of size at most $10n/21$. Equivalently, every $n$ vertex triangulation has a spanning tree with at least $11n/21$ leaves. Prior to the current work, the best known bounds were $n/2$, which follows from work of Albertson, Berman, Hutchinson, and Thomassen (J. Graph Theory \textbf{
Prosenjit Bose +4 more
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Connected domination in grid graphs
CoRR, 2021 44 ...
Masahisa Goto, Koji M. Kobayashi
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Triple Connected Domination Number of a Graph [PDF]
, 2012 The concept of triple connected graphs with real life application was introduced by considering the existence of a path containing any three vertices of a graph G.
Selvam Avadayappan +7 more
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