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 (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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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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A note on lower bounds for the total domination number of digraphs
, 2017 A vertex subset S of a digraph D is called a dominating set of D if every vertex not in S is adjacent from at least one vertex in S. A dominating set S of D is called a total dominating set of D if the subdigraph of D induced by S has no isolated ...
Chen, Xiaodan, Hao, Guoliang
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Cubic Graphs with Total Domatic Number at Least Two
Discussiones Mathematicae Graph Theory, 2018 Let G be a graph with no isolated vertex. A total dominating set of G is a set S of vertices of G such that every vertex is adjacent to at least one vertex in S.
Akbari Saieed +3 more
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Global Italian domination in graphs
, 2019 An Italian dominating function (IDF) on a graph G = (V,E) is a function f : V → f{0, 1, 2} satisfying the condition that for every vertex v ∈ V (G) with f(v) = 0, either v is adjacent to a vertex assigned 2 under f, or v is adjacent to at least two ...
Xu, Zhijun +3 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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Improved McClelland and Koolen-Moulton bounds for distance energy of a graph. [PDF]
J Inequal Appl, 2018 Sridhara G +3 more
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On the characterization of claw-free graphs with given total restrained domination number. [PDF]
Springerplus, 2016 Pi X.
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Extremal values on Zagreb indices of trees with given distance k-domination number. [PDF]
J Inequal Appl, 2018 Pei L, Pan X.
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