Results 21 to 30 of about 477 (116)
A Note on the Locating-Total Domination in Graphs
Discussiones Mathematicae Graph Theory, 2017 In this paper we obtain a sharp (improved) lower bound on the locating-total domination number of a graph, and show that the decision problem for the locating-total domination is NP-complete.
Miller Mirka +4 more
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Power Domination in Knödel Graphs and Hanoi Graphs
Discussiones Mathematicae Graph Theory, 2018 In this paper, we study the power domination problem in Knödel graphs WΔ,2ν and Hanoi graphs Hpn$H_p^n $ . We determine the power domination number of W3,2ν and provide an upper bound for the power domination number of Wr+1,2r+1 for r ≥ 3.
Varghese Seethu +2 more
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, 2015 Let G = (V (G), E(G)) be an arbitrary graph and let X ⊆ V (G). The set A(X) = X ∩ N(X) consists of the non-isolates in X, where N(X) = {y ∈ V (G) : yx ∈ E(G) for some x ∈ X}. Let B(X) denote the set of vertices in V (G)\X that has a neighbor in X.
C. Armada, S. Canoy
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A Characterization for 2-Self-Centered Graphs
Discussiones Mathematicae Graph Theory, 2018 A graph is called 2-self-centered if its diameter and radius both equal to 2. In this paper, we begin characterizing these graphs by characterizing edge-maximal 2-self-centered graphs via their complements.
Shekarriz Mohammad Hadi +2 more
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Total Roman domination on the digraphs
Open Mathematics, 2023 Let D=(V,A)D=\left(V,A) be a simple digraph with vertex set VV, arc set AA, and no isolated vertex. A total Roman dominating function (TRDF) of DD is a function h:V→{0,1,2}h:V\to \left\{0,1,2\right\}, which satisfies that each vertex x∈Vx\in V with h(x ...
Zhang Xinhong, Song Xin, Li Ruijuan
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Restrained convex dominating sets in the corona and the products of graphs
, 2015 In this paper, we characterize the restrained convex dominating sets in the corona, lexicographic and Cartesian products of two connected graphs and then determine the corresponding restrained convex domination numbers of these graphs.
Enrico L. Enriquez, S. Canoy
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Bounding the Open k-Monopoly Number of Strong Product Graphs
Discussiones Mathematicae Graph Theory, 2018 Let G = (V, E) be a simple graph without isolated vertices and minimum degree δ, and let k ∈ {1 − ⌈δ/2⌉, . . . , ⌊δ/2⌋} be an integer. Given a set M ⊂ V, a vertex v of G is said to be k-controlled by M if δM(v)≥δG(v)2+k$\delta _M (v) \ge {{\delta _G (v)}
Kuziak Dorota +2 more
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Discussiones Mathematicae Graph Theory, 2020 If S = (a1, a2, . . .) is a non-decreasing sequence of positive integers, then an S-packing coloring of a graph G is a partition of V (G) into sets X1, X2, . . .
Brešar Boštjan +3 more
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Unique Strong Isolate Semitotal Domination in Graphs
Indian Journal of Science and TechnologyObjective: This study introduces a new domination parameter called “Unique strong isolate semitotal domination”. Methods: A unique strong isolated semitotal dominating set(USISTD-set) D of a graph G is an isolated semitotal dominating set(ISTD-set) in ...
Sivagnanam Mutharasu, D. Nithya
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Secure Domination in Lict Graphs
, 2018 For any graph G = (V,E), lict graph η(G) of a graph G is the graph whose vertex set is the union of the set of edges and the set of cut-vertices of G in which two vertices are adjacent if and only if the corresponding edges are adjacent or the ...
Girish V. Rajasekharaiah +2 more
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