Locating-Total Domination Number in Strong Product of Two Paths

Abstract

In a monitoring system, each node's status is unique, and the system can accurately locate the node when there is a problem, which can be modeled through graphs’ locating-total domination. When laying out the monitoring system, it is crucial to select the root node. Given a graph G, its locating-total domination number is the minimum cardinality of G’s locating-total dominating set. In this paper, we give the bounds of this number for the strong product of two paths