Results 11 to 20 of about 5,986,669 (282)
Connected Dominating Sets in Triangulations
CoRR, 2023 A dominating set of a graph G is connected if it induces a connected graph in G. For planar triangulations, it has been known since 1990 that every n-vertex triangulation admits a connected dominating set of size at most n/2 − 1, and no improvement to this bound was known for over three decades.
Bose, Prosenjit +4 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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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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Dominating Sets and Connected Dominating Sets in Dynamic Graphs [PDF]
CoRR, 2019 In this paper we study the dynamic versions of two basic graph problems: Minimum Dominating Set and its variant Minimum Connected Dominating Set. For those two problems, we present algorithms that maintain a solution under edge insertions and edge deletions in time $O(Δ\cdot \text{polylog}~n)$ per update, where $Δ$ is the maximum vertex degree in the ...
Hjuler N. +3 more
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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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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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Performance of Connected Dominating Set in OLSR protocol [PDF]
, 2004 We analyze the performance of connected dominating set (CDS)election protocols in wireless ad hoc networks. We compare the dominating set made from MPR and a new connected dominating set (NCDS) protocols issued from a straightforward generalization of ...
Jacquet, Philippe
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Approximation algorithms for connected dominating sets [PDF]
Algorithmica, 1996 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Guha, Sudipto, Khuller, Samir
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On the Parameterized Complexity of Reconfiguration of Connected Dominating Sets [PDF]
Algorithmica, 2022 In a reconfiguration version of an optimization problem $\mathcal{Q}$ the input is an instance of $\mathcal{Q}$ and two feasible solutions $S$ and $T$. The objective is to determine whether there exists a step-by-step transformation between $S$ and $T$ such that all intermediate steps also constitute feasible solutions.
Daniel Lokshtanov +3 more
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Algorithmic Aspects of Secure Connected Domination in Graphs
Discussiones Mathematicae Graph Theory, 2021 Let G = (V, E) be a simple, undirected and connected graph. A connected dominating set S ⊆ V is a secure connected dominating set of G, if for each u ∈ V \ S, there exists v ∈ S such that (u, v) ∈ E and the set (S \ {v}) ∪ {u} is a connected dominating ...
Kumar Jakkepalli Pavan +1 more
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