Results 1 to 10 of about 1,519 (103)
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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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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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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Some Progress on the Double Roman Domination in Graphs
Discussiones Mathematicae Graph Theory, 2019 For a graph G = (V,E), a double Roman dominating function (or just DRDF) is a function f : V → {0, 1, 2, 3} having the property that if f(v) = 0 for a vertex v, then v has at least two neighbors assigned 2 under f or one neighbor assigned 3 under f, and ...
Rad Nader Jafari, Rahbani Hadi
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On the general position number of two classes of graphs
Open Mathematics, 2022 The general position problem is to find the cardinality of the largest vertex subset SS such that no triple of vertices of SS lies on a common geodesic.
Yao Yan, He Mengya, Ji Shengjin
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Connected 𝐷 - Eccentric Domination in Graphs
Indian Journal of Science and TechnologyObjectives: To introduce connected -eccentric point set, connected -eccentric number, connected -eccentric dominating set, connected -eccentric domination number in a graph and related concepts. Methods: -distance in graphs are used to find the connected
A. Prasanna, N. Mohamedazarudeen
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