Computing [1; 2]-open locating domination number in some families of graphs
Abstract
The problem of location detection is investigated for many scenarios, such as pointing out the flaws in the multiprocessors, invaders in buildings and facilities, and utilizing wireless sensors networks for the environmental monitoring process. The system or structure can be illustrated as a graph in each of these applications, and sensors strategically placed at a subset of vertices can determine and identify irregularities within the network. The (OLD-set) that is open locating dominating set is a subset of vertices in a graph, such that every vertex within the graph is distinct and non-empty. Let G = (V; E), be the graph, a set S ? V (G) is a [1; 2]-OLD set if N(i) \ S 6= ;, for some i 2 V (G), and 1 ? jN(i)\Sj ? 2, as well as N(i)\S 6= N(j)\S, for every pair of distinct vertices i; j 2 V (G)nS. The minimum cardinality of [1; 2]-OLD set in a graph G is called [1; 2]-open locating domination number and is denoted by ?[1 old ;2]. In this paper, we compute the [1; 2]-open locating domination number of some families of graphs.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2023 Tianlei Zhu, Yingke Yang, Shu Bao, Hassan Raza
This work is licensed under a Creative Commons Attribution 4.0 International License.