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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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Graphs whose vertex set can be partitioned into a total dominating set and an independent dominating set [PDF]
Opuscula MathematicaA graph \(G\) whose vertex set can be partitioned into a total dominating set and an independent dominating set is called a TI-graph. We give constructions that yield infinite families of graphs that are TI-graphs, as well as constructions that yield ...
Teresa W. Haynes, Michael A. Henning
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On the dominating set polytope
European Journal of Combinatorics, 2008 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Bouchakour, Mustapha +3 more
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Journal of Graph Theory, 1994 AbstractLet G = (V, E) be a connected graph. A set D ⊂ V is a set‐dominating set (sd‐set) if for every set T ⊂ V − D, there exists a nonempty set S ⊂ D such that the subgraph 〈S ∪ T〉 induced by S ∪ T is connected. The set‐domination number γs(G) of G is the minimum cardinality of a sd‐set.
E. Sampathkumar 0001, L. Pushpalatha
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Distributed dominating sets on grids [PDF]
2013 American Control Conference, 2013 10 pages, 9 figures, accepted in ACC ...
Elaheh Fata +2 more
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Domination, Eternal Domination, and Clique Covering
Discussiones Mathematicae Graph Theory, 2015 Eternal and m-eternal domination are concerned with using mobile guards to protect a graph against infinite sequences of attacks at vertices. Eternal domination allows one guard to move per attack, whereas more than one guard may move per attack in the m-
Klostermeyer William F., Mynhardt C.M.
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Some results on domination in annihilating-ideal graphs of commutative rings [PDF]
Journal of Hyperstructures. Let R be a commutative ring with identity and A(R) be the set of all ideals of R with non-zero annihilators. The annihilating-ideal graph of R is defined as the graph AG(R) with the vertex set A∗(R) = A(R)\{(0)} and two distinct vertices I and J are ...
Reza Taheri
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DOMINATING SET ON CHAIN OF FUZZY GRAPHS
Tikrit Journal of Pure Science, 2023 In this paper, we define fuzzy graph chains, which comprise vertex identification. These fuzzy graphs are isomorphic fuzzy graphs, provide that after applying various features to the chain of fuzzy graphs, which as special fuzzy graph chain of .
Russel H. Majeed, Nabeel E. Arif
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On the complexity of some hop domination parameters
Electronic Journal of Graph Theory and Applications, 2019 A hop Roman dominating function (HRDF) on a graph G = (V, E) is a function f : V → {0, 1, 2} having the property that for every vertex v ∈ V with f(v) = 0 there is a vertex u with f(u) = 2 and d(u, v) = 2. The weight of an HRDF f is the sum of its values
Nader Jafari Rad, Elahe Shabani
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Eternal Domination: Criticality and Reachability
Discussiones Mathematicae Graph Theory, 2017 We show that for every minimum eternal dominating set, D, of a graph G and every vertex v ∈ D, there is a sequence of attacks at the vertices of G which can be defended in such a way that an eternal dominating set not containing v is reached.
Klostermeyer William F. +1 more
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