Results 61 to 70 of about 477 (116)
Changing and Unchanging of the Domination Number of a Graph: Path Addition Numbers
Discussiones Mathematicae Graph Theory, 2021 Given a graph G =(V, E) and two its distinct vertices u and v, the (u, v)-Pk-addition graph of G is the graph Gu,v,k−2 obtained from disjoint union of G and a path Pk : x0, x1,...,xk−1, k ≥ 2, by identifying the vertices u and x0, and identifying the ...
Samodivkin Vladimir
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Secure convex dominating sets in corona of graphs
, 2015 In this paper, we characterize the secure convex dominating sets in the corona of two connected graphs and then determine the corresponding secure convex domination numbers of these graphs.
Enrico L. Enriquez
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Independent Transversal Total Domination Versus Total Domination in Trees
Discussiones Mathematicae Graph Theory, 2021 A subset of vertices in a graph G is a total dominating set if every vertex in G is adjacent to at least one vertex in this subset. The total domination number of G is the minimum cardinality of any total dominating set in G and is denoted by γt(G).
Martínez Abel Cabrera +2 more
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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 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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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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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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