Computing [1; 2]-open locating domination number in some families of graphs

Authors

  • Tianlei Zhu Department of Mathematics, Wenzhou-Kean University, Wenzhou, 325060, China
  • Yingke Yang Department of Mathematics, Wenzhou-Kean University, Wenzhou, 325060, China
  • Shu Bao Department of Mathematics, Wenzhou-Kean University, Wenzhou, 325060, China
  • Hassan Raza Department of Mathematics, Wenzhou-Kean University, Wenzhou, 325060, China

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.

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Published

2022-06-30

How to Cite

Zhu, T., Yang, Y., Bao, S., & Raza, H. (2022). Computing [1; 2]-open locating domination number in some families of graphs. International Journal of Advancements in Mathematics, 2(1), 33–49. Retrieved from https://www.scienceimpactpub.com/journals/index.php/IJAM/article/view/535