Results 11 to 20 of about 14,864 (300)
Making a Dominating Set of a Graph Connected
Discussiones Mathematicae Graph Theory, 2018 Let G = (V,E) be a graph and S ⊆ V. We say that S is a dominating set of G, if each vertex in V \ S has a neighbor in S. Moreover, we say that S is a connected (respectively, 2-edge connected or 2-connected) dominating set of G if G[S] is connected ...
Li Hengzhe, Wu Baoyindureng, Yang Weihua
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Minimum Connected Dominating Sets of Random Cubic Graphs [PDF]
The Electronic Journal of Combinatorics, 2002 We present a simple heuristic for finding a small connected dominating set of cubic graphs. The average-case performance of this heuristic, which is a randomised greedy algorithm, is analysed on random $n$-vertex cubic graphs using differential equations.
William Duckworth
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A Linear Kernel for Planar Connected Dominating Set [PDF]
Theoretical Computer Science, 2010 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Daniel Lokshtanov +2 more
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Proper connection number and connected dominating sets [PDF]
Theoretical Computer Science, 2015 The proper connection number $pc(G)$ of a connected graph $G$ is defined as the minimum number of colors needed to color its edges, so that every pair of distinct vertices of $G$ is connected by at least one path in $G$ such that no two adjacent edges of the path are colored the same, and such a path is called a proper path. In this paper, we show that
Xueliang Li, Meiqin Wei, Jun Yue
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Approximating k-Connected m-Dominating Sets [PDF]
Algorithmica, 2022 A subset $S$ of nodes in a graph $G$ is a $k$-connected $m$-dominating set ($(k,m)$-cds) if the subgraph $G[S]$ induced by $S$ is $k$-connected and every $v \in V \setminus S$ has at least $m$ neighbors in $S$. In the $k$-Connected $m$-Dominating Set ($(k,m)$-CDS) problem the goal is to find a minimum weight $(k,m)$-cds in a node-weighted graph. For $m
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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 ...
Chandran, L. Sunil +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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Connected domination value in graphs
Electronic Journal of Graph Theory and Applications, 2021 In a connected graph G = (V,E), a set D ⊂ V is a connected dominating set if for every vertex v ∈ V \ D, there exists u ∈ D such that u and v are adjacent, and the subgraph〈D〉induced by D in G is connected.
Angsuman Das
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Forcing Parameters in Fully Connected Cubic Networks
Mathematics, 2022 Domination in graphs has been extensively studied and adopted in many real life applications. The monitoring electrical power system is a variant of a domination problem called power domination problem.
Yongsheng Rao +4 more
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Energy Efficient Algorithm of Constructing Connected Dominating Set in WSN [PDF]
Jisuanji gongcheng, 2017 The existing methods of constructing Connected Dominating Set (CDS) have some drawbacks,such as redundant steps,much more energy consumption,and not adapting to the changes of dynamic network topology.So this paper proposes an improved algorithm called ...
JI Fusheng,WU Chen,LIU Qiaoshou
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