Results 31 to 40 of about 228 (85)
Bounds on Watching and Watching Graph Products
Discussiones Mathematicae Graph Theory, 2022 A watchman’s walk for a graph G is a minimum-length closed dominating walk, and the length of such a walk is denoted (G). We introduce several lower bounds for such walks, and apply them to determine the length of watchman’s walks in several grids.
Dyer Danny, Howell Jared
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Improving the Efficiency of Fuzzy Graphs and Their Complements Using Some Influencing Parameters
Journal of Mathematics, Volume 2025, Issue 1, 2025.This study focuses on constructing optimal network structures for fuzzy graph (FG) products. In graph theory, the complement of a FG product is essential since it analyses alternate interactions between the vertices. Such a complement is used to represent situations in which specific connections are deliberately excluded, which helps to understand ...
A. Meenakshi +4 more
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On The Total Roman Domination in Trees
Discussiones Mathematicae Graph Theory, 2019 A total Roman dominating function on a graph G is a function f : V (G) → {0, 1, 2} satisfying the following conditions: (i) every vertex u for which f(u) = 0 is adjacent to at least one vertex v for which f(v) = 2 and (ii) the subgraph of G induced by ...
Amjadi Jafar +2 more
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On Well-Covered Direct Products
Discussiones Mathematicae Graph Theory, 2022 A graph G is well-covered if all maximal independent sets of G have the same cardinality. In 1992 Topp and Volkmann investigated the structure of well-covered graphs that have nontrivial factorizations with respect to some of the standard graph products.
Kuenzel Kirsti, Rall Douglas F.
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A Study on Variants of Status Unequal Coloring in Graphs and Its Properties
Journal of Mathematics, Volume 2024, Issue 1, 2024.Let G∧ be a simple connected graph with vertex set ϑG∧ and edge set ξG∧. The status of a vertex p∈ϑG∧ is defined as ∑q≠pd(p, q). A subset P of ϑG∧ is called a status unequal dominating set (stu‐dominating set) of G∧; for every q∈ϑ−P, there exists p in P such that p and q are adjacent and st(p) ≠ st(q).
Parvathy Gnana Sambandam +4 more
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Bipartite graphs with close domination and k-domination numbers
Open Mathematics, 2020 Let kk be a positive integer and let GG be a graph with vertex set V(G)V(G). A subset D⊆V(G)D\subseteq V(G) is a kk-dominating set if every vertex outside DD is adjacent to at least kk vertices in DD. The kk-domination number γk(G){\gamma }_{k}(G) is the
Ekinci Gülnaz Boruzanlı +1 more
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Journal of Mathematics, Volume 2024, Issue 1, 2024.A perfect Roman {3}‐dominating function on a graph G = (V, E) is a function f : V⟶{0, 1, 2, 3} having the property that if f(v) = 0, then ∑u∈N(v)f(u) = 3, and if f(v) = 1, then ∑u∈N(v)f(u) = 2 for any vertex v ∈ V. The weight of a perfect Roman {3}‐dominating function f is the sum ∑v∈Vf(v).
Ahlam Almulhim, Santi Spadaro
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A Constructive Characterization of Vertex Cover Roman Trees
Discussiones Mathematicae Graph Theory, 2021 A Roman dominating function on a graph G = (V (G), E(G)) is a function f : V (G) → {0, 1, 2} satisfying the condition that every vertex u for which f (u) = 0 is adjacent to at least one vertex v for which f (v) = 2.
Martínez Abel Cabrera +2 more
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Changing and Unchanging of the Domination Number of a Graph: Path Addition Numbers
Discussiones Mathematicae Graph Theory, 2021 Given a graph G =(V, E) and two its distinct vertices u and v, the (u, v)-Pk-addition graph of G is the graph Gu,v,k−2 obtained from disjoint union of G and a path Pk : x0, x1,...,xk−1, k ≥ 2, by identifying the vertices u and x0, and identifying the ...
Samodivkin Vladimir
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Independent Transversal Total Domination Versus Total Domination in Trees
Discussiones Mathematicae Graph Theory, 2021 A subset of vertices in a graph G is a total dominating set if every vertex in G is adjacent to at least one vertex in this subset. The total domination number of G is the minimum cardinality of any total dominating set in G and is denoted by γt(G).
Martínez Abel Cabrera +2 more
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