Author:
Cabaro Jean Mansanadez,Rara Helen
Abstract
Let G be a connected graph. An ordered set of vertices {v1, ..., vl} is a 2-resolving set for G if, for any distinct vertices u, w ∈ V (G), the lists of distances (dG(u, v1), ..., dG(u, vl)) and (dG(w, v1), ..., dG(w, vl)) differ in at least 2 positions. A 2-resolving set S ⊆ V (G) which isdominating is called a 2-resolving dominating set or simply 2R-dominating set in G. The minimum cardinality of a 2-resolving dominating set in G, denoted by γ2R(G), is called the 2R-domination number of G. Any 2R-dominating set of cardinality γ2R(G) is then referred to as a γ2R-set in G. This study deals with the concept of 2-resolving dominating set of a graph. It characterizes the 2-resolving dominating set in the join, corona and lexicographic product of two graphs and determine the bounds or exact values of the 2-resolving dominating number of these graphs.
Publisher
New York Business Global LLC
Subject
Applied Mathematics,Geometry and Topology,Numerical Analysis,Statistics and Probability,Algebra and Number Theory,Theoretical Computer Science
Cited by
5 articles.
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1. $1$-movable $2$-Resolving Hop Domination in Graph;European Journal of Pure and Applied Mathematics;2023-07-30
2. Outer-Connected 2-Resolving Hop Domination in Graphs;European Journal of Pure and Applied Mathematics;2023-04-30
3. 1-Movable Resolving Hop Domination in Graphs;European Journal of Pure and Applied Mathematics;2023-01-29
4. Restrained 2-Resolving Hop Domination in Graphs;European Journal of Pure and Applied Mathematics;2023-01-29
5. On 2-Resolving Hop Dominating Sets in the Join, Corona and Lexicographic Product of Graphs;European Journal of Pure and Applied Mathematics;2022-10-31