Results 61 to 70 of about 1,497 (106)
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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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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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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On (k1A1, k2A2, k3A3)-Edge Colourings in Graphs and Generalized Jacobsthal Numbers
Annales Mathematicae SilesianaeIn this paper we introduce a new kind of generalized Jacobsthal numbers in a distance sense. We give the identities and matrix representations for them and their connections with the Fibonacci and the Pell numbers. We also describe the interpretations of
Piejko Krzysztof, Trojnar-Spelina Lucyna
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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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On The Co-Roman Domination in Graphs
Discussiones Mathematicae Graph Theory, 2019 Let G = (V, E) be a graph and let f : V (G) → {0, 1, 2} be a function. A vertex v is said to be protected with respect to f, if f(v) > 0 or f(v) = 0 and v is adjacent to a vertex of positive weight. The function f is a co-Roman dominating function if (i)
Shao Zehui +4 more
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Andronov-Hopf and Neimark-Sacker bifurcations in time-delay differential equations and difference equations with applications to models for diseases and animal populations. [PDF]
Adv Differ Equ, 2020 Darlai R, Moore EJ, Koonprasert S.
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