Results 1 to 10 of about 1,497 (106)
Reinforcement Number of a Graph with respect to Half-Domination
Journal of Mathematics, 2021 In this paper, we introduce the concept of reinforcement number with respect to half-domination and initiate a study on this parameter. Furthermore, we obtain various upper bounds for this parameter. AMS subject classification: 05C38, 05C40, 05C69.
G. Muhiuddin +4 more
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Further Results on Packing Related Parameters in Graphs
Discussiones Mathematicae Graph Theory, 2022 Given a graph G = (V, E), a set B ⊆ V (G) is a packing in G if the closed neighborhoods of every pair of distinct vertices in B are pairwise disjoint. The packing number ρ(G) of G is the maximum cardinality of a packing in G. Similarly, open packing sets
Mojdeh Doost Ali +2 more
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A Classification of Cactus Graphs According to their Domination Number
Discussiones Mathematicae Graph Theory, 2022 A set S of vertices in a graph G is a dominating set of G if every vertex not in S is adjacent to some vertex in S. The domination number, γ(G), of G is the minimum cardinality of a dominating set of G.
Hajian Majid +2 more
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Roman {2}-Domination Problem in Graphs
Discussiones Mathematicae Graph Theory, 2022 For a graph G = (V, E), a Roman {2}-dominating function (R2DF) f : V → {0, 1, 2} has the property that for every vertex v ∈ V with f(v) = 0, either there exists a neighbor u ∈ N(v), with f(u) = 2, or at least two neighbors x, y ∈ N(v) having f(x) = f(y) =
Chen Hangdi, Lu Changhong
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Journal of Education College Wasit University, 2021 Let {\ \ \gamma}^e(G) be the edge domination number of a graph. A “web graph” W(s,t) is obtained from the Cartesian product of cycle graph of order s\ and path graph of order\ t.
A. Omran, M. Al-Harere
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Domination Number, Independent Domination Number and 2-Independence Number in Trees
Discussiones Mathematicae Graph Theory, 2021 For a graph G, let γ(G) be the domination number, i(G) be the independent domination number and β2(G) be the 2-independence number. In this paper, we prove that for any tree T of order n ≥ 2, 4β2(T) − 3γ(T) ≥ 3i(T), and we characterize all trees ...
Dehgardi Nasrin +4 more
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Restrained Domination in Self-Complementary Graphs
Discussiones Mathematicae Graph Theory, 2021 A self-complementary graph is a graph isomorphic to its complement. A set S of vertices in a graph G is a restrained dominating set if every vertex in V(G) \ S is adjacent to a vertex in S and to a vertex in V(G) \ S.
Desormeaux Wyatt J. +2 more
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Total Domination in Generalized Prisms and a New Domination Invariant
Discussiones Mathematicae Graph Theory, 2021 In this paper we complement recent studies on the total domination of prisms by considering generalized prisms, i.e., Cartesian products of an arbitrary graph and a complete graph.
Tepeh Aleksandra
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Spanning Trees with Disjoint Dominating and 2-Dominating Sets
Discussiones Mathematicae Graph Theory, 2022 In this paper, we provide a structural characterization of graphs having a spanning tree with disjoint dominating and 2-dominating sets.
Miotk Mateusz, Żyliński Paweł
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The Slater and Sub-k-Domination Number of a Graph with Applications to Domination and k-Domination
Discussiones Mathematicae Graph Theory, 2020 In this paper we introduce and study a new graph invariant derived from the degree sequence of a graph G, called the sub-k-domination number and denoted subk(G).
Amos David +3 more
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