Results 41 to 50 of about 477 (116)
On Independent Domination in Planar Cubic Graphs
Discussiones Mathematicae Graph Theory, 2019 A set S of vertices in a graph G is an independent dominating set of G if S is an independent set and every vertex not in S is adjacent to a vertex in S.
Abrishami Gholamreza +2 more
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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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Exact Dominion of the Prism Graph: Enumeration by Congruence Class via Cyclic Words
International Journal of Mathematics and Mathematical Sciences, Volume 2026, Issue 1, 2026.Let Gn = Cn□P2 be the prism graph on 2n vertices. The dominion ζ(Gn) counts the minimum dominating sets of Gn. Encoding column selections as cyclic words over a quaternary alphabet converts domination into explicit local adjacency constraints, reducing the count of minimum dominating sets to the enumeration of minimum‐weight admissible words.
Julian Allagan +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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Selection of an Optimal Warehouses Using Global Regular Domination in Graphs
International Journal of Mathematics and Mathematical Sciences, Volume 2025, Issue 1, 2025.Let G = (V, E) be a simple graph. A subset S of V (G) is said to be global dominating set if S is a dominating set of the given graph G and its complement G. A subset whose induced subgraph is regular in G is also regular in G. A dominating set D of V (G) is called a regular dominating set if hSi is regular. In this article, we introduce global regular
R. Sundareswaran +6 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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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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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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On pairs of disjoint dominating sets in a graph
, 2016 In this paper, we investigate pairs of disjoint dominating sets A and B in a graph G, where B is either an independent or a total dominating set in G.
Edward Kiunisala, Ferdinand P. Jamil
semanticscholar +1 more source