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Dominating Sets and Connected Dominating Sets in Dynamic Graphs [PDF]
, 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 $O( \cdot \text{polylog}~n)$ per update, where $ $ is the maximum vertex degree in the
Hjuler N. +3 more
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Enumerating Connected Dominating Sets
, 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.
Abu-Khzam, Faisal +4 more
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Approximation algorithms for connected dominating sets [PDF]
Algorithmica, 1996 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Guha, S., Khuller, S.
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Perfect Outer-connected Domination in the Join and Corona of Graphs
Recoletos Multidisciplinary Research Journal, 2016 Let ๐บ be a connected simple graph. A dominating set ๐ โ ๐(๐บ) is called a perfect dominating set of ๐บ if each ๐ข โ ๐ ๐บ โ ๐ is dominated by exactly one element of ๐.
Enrico Enriquez +3 more
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Inverse Domination Parameters of Jump Graph
Ratio Mathematica, 2023 Let G=(V,E)\ be a connected graph. Let D be a minimum dominating set in G.\ If V-D contains a dominating set D^\prime of G, then D^\prime is called an inverse dominating set with respect to D.
S Santha, G.T Krishna Veni
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Below all subsets for Minimal Connected Dominating Set [PDF]
SIAM Journal on Discrete Mathematics, 2016 A vertex subset $S$ in a graph $G$ is a dominating set if every vertex not contained in $S$ has a neighbor in $S$. A dominating set $S$ is a connected dominating set if the subgraph $G[S]$ induced by $S$ is connected. A connected dominating set $S$ is a minimal connected dominating set if no proper subset of $S$ is also a connected dominating set.
Daniel Lokshtanov +2 more
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Connected Dominating Sets [PDF]
, 2009 Wireless sensor networks (WSNs) are now widely used in many applications. However, routing in WSNs is very challenging due to the inherent characteristics that distinguish these networks from other wireless networks. The concept of hierarchical routing is widely used to perform energy-efficient routing in WSNs.
Yiwei Wu, Yingshu Li
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Algorithmic complexity of secure connected domination in graphs
AKCE International Journal of Graphs and Combinatorics, 2020 Let be a simple, undirected, and connected graph. A connected (total) dominating set is a secure connected (total) dominating set of G, if for each there exists such that and is a connected (total) dominating set of G. The minimum cardinality of a secure
J. Pavan Kumar +2 more
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Linear separation of connected dominating sets in graphs
Ars Mathematica Contemporanea, 2016 32 pages, 8 ...
Nina Chiarelli, Martin Milaniฤ
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Connected Dominating Sets in Triangulations
, 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{
Bose, Prosenjit +4 more
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