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Average distance and connected domination
AKCE International Journal of Graphs and Combinatorics, 2023 We give a tight upper bound on the average distance of a connected graph of given order in terms of its connected domination number. Our results are a strengthening of a result by DeLaViña, Pepper, and Waller [A note on dominating sets and average ...
P. Mafuta, S. Mukwembi
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Generalized connected domination in graphs [PDF]
Discrete Mathematics & Theoretical Computer Science, 2006 As a generalization of connected domination in a graph G we consider domination by sets having at most k components. The order γ c k (G) of such a smallest set we relate to γ c (G), the order of a smallest connected dominating set. For a tree
M. Kouider, P.D. Vestergaard
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On graphs with equal total domination and connected domination numbers [PDF]
Applied Mathematics Letters, 2006 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Xuegang Chen
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Characterization of graphs with equal domination and connected domination numbers [PDF]
Discrete Mathematics, 2004 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Xuegang Chen
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On weakly connected domination in graphs II [PDF]
Discrete Mathematics, 2005 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Johannes H Hattingh
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Connected domination value in graphs [PDF]
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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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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Connected power domination in graphs [PDF]
Journal of Combinatorial Optimization, 2019 The study of power domination in graphs arises from the problem of placing a minimum number of measurement devices in an electrical network while monitoring the entire network. A power dominating set of a graph is a set of vertices from which every vertex in the graph can be observed, following a set of rules for power system monitoring. In this paper,
Logan Smith +2 more
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Traceability of connected domination critical graphs [PDF]
Applied Mathematics and Computation, 2020 A dominating set in a graph $G$ is a set $S$ of vertices of $G$ such that every vertex outside $S$ is adjacent to a vertex in $S$. A connected dominating set in $G$ is a dominating set $S$ such that the subgraph $G[S]$ induced by $S$ is connected. The connected domination number of $G$, $γ_c(G)$, is the minimum cardinality of a connected dominating set
Michael Henning +2 more
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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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