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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
Applied Mathematics Letters, 2006 A subset S of V is called a total dominating set if every vertex in V is adjacent to some vertex in S. The total domination number γt(G) of G is the minimum cardinality taken over all total dominating sets of G.
Xue-Gang Chen
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Characterization of graphs with equal domination and connected domination numbers
Discrete Mathematics, 2004 Arumugam and Paulraj Joseph (Discrete Math 206 (1999) 45) have characterized trees, unicyclic graphs and cubic graphs with equal domination and connected domination numbers.
Xue-Gang Chen
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Connected domination game played on Cartesian products
Open Mathematics, 2019 The connected domination game on a graph G is played by Dominator and Staller according to the rules of the standard domination game with the additional requirement that at each stage of the game the selected vertices induce a connected subgraph of G. If
Bujtás Csilla +3 more
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Total connected domination game [PDF]
Opuscula Mathematica, 2021 The (total) connected domination game on a graph \(G\) is played by two players, Dominator and Staller, according to the standard (total) domination game with the additional requirement that at each stage of the game the selected vertices induce a ...
Csilla Bujtás +3 more
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Connected 2- Dominating Sets and Connected 2- Domination Polynomials of the Complete Bipartite Graph k_(2,m) [PDF]
Ratio Mathematica, 2022 Let be a simple graph.Let be the family of connected 2 dominating sets in with cardinality and |.Then the polynomial is called the 2 domination polynomial of where is the connected 2 domination number of Let be the family of connected 2 dominating ...
Y.A. Shiny, Anithababy T
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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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Weakly connected domination critical graphs [PDF]
Opuscula Mathematica, 2008 A dominating set \(D \subset V(G)\) is a weakly connected dominating set in \(G\) if the subgraph \(G[D]_w = (N_{G}[D],E_w)\) weakly induced by \(D\) is connected, where \(E_w\) is the set of all edges with at least one vertex in \(D\).
Magdalena Lemańska, Agnieszka Patyk
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Total outer-connected domination numbers of trees
Discrete Applied Mathematics, 2009 Let G=(V,E) be a graph without an isolated vertex. A set D⊆V(G) is a total dominating set if D is dominating, and the induced subgraph G[D] does not contain an isolated vertex.
Joanna Cyman, Joanna Raczek
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