Results 41 to 50 of about 228 (85)
Sufficient Conditions for a Digraph to Admit A (1, ≤ ℓ)-Identifying Code
Discussiones Mathematicae Graph Theory, 2021 A (1, ≤ ℓ)-identifying code in a digraph D is a subset C of vertices of D such that all distinct subsets of vertices of cardinality at most ℓ have distinct closed in-neighbourhoods within C. In this paper, we give some sufficient conditions for a digraph
Balbuena Camino +2 more
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Power Domination in the Generalized Petersen Graphs
Discussiones Mathematicae Graph Theory, 2020 The problem of monitoring an electric power system by placing as few measurement devices in the system can be formulated as a power dominating set problem in graph theory.
Zhao Min, Shan Erfang, Kang Liying
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On Nordhaus-Gaddum type relations of δ-complement graphs. [PDF]
Heliyon, 2023 Vichitkunakorn P +2 more
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Domination Parameters of a Graph and its Complement
Discussiones Mathematicae Graph Theory, 2018 A dominating set in a graph G is a set S of vertices such that every vertex in V (G) \ S is adjacent to at least one vertex in S, and the domination number of G is the minimum cardinality of a dominating set of G.
Desormeaux Wyatt J. +2 more
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On the spectrum, energy and Laplacian energy of graphs with self-loops. [PDF]
Heliyon, 2023 Preetha P U, Suresh M, Bonyah E.
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On Accurate Domination in Graphs
Discussiones Mathematicae Graph Theory, 2019 A dominating set of a graph G is a subset D ⊆ VG such that every vertex not in D is adjacent to at least one vertex in D. The cardinality of a smallest dominating set of G, denoted by γ(G), is the domination number of G. The accurate domination number of
Cyman Joanna +2 more
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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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Bounds on the Locating-Domination Number and Differentiating-Total Domination Number in Trees
Discussiones Mathematicae Graph Theory, 2018 A subset S of vertices in a graph G = (V,E) is a dominating set of G if every vertex in V − S has a neighbor in S, and is a total dominating set if every vertex in V has a neighbor in S.
Rad Nader Jafari, Rahbani Hadi
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Total Domination Versus Paired-Domination in Regular Graphs
Discussiones Mathematicae Graph Theory, 2018 A subset S of vertices of a graph G is a dominating set of G if every vertex not in S has a neighbor in S, while S is a total dominating set of G if every vertex has a neighbor in S. If S is a dominating set with the additional property that the subgraph
Cyman Joanna +4 more
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Reconfiguring Minimum Dominating Sets: The γ-Graph of a Tree
Discussiones Mathematicae Graph Theory, 2018 We consider γ-graphs, which are reconfiguration graphs of the minimum dominating sets of a graph G. We answer three open questions about γ- graphs of trees by providing upper bounds on the maximum degree, the diameter, and the number of minimum ...
Edwards Michelle +2 more
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