On study of some bounds for fault-tolerant metric dimension and adjacency fault-tolerant resolving set of corona product graphs
Muhammad Asif Shahzad, Nasir A Ali, Suhad Ali Osman Abdallah, Nashaat S. Abd El-Gawaad · Discrete Mathematics Algorithms and Applications · 2024
In this paper, we investigate bounds for the fault-tolerant metric dimension and adjacency fault-tolerant resolving set of corona product graphs. Let [Formula: see text] and [Formula: see text] be two graphs with orders [Formula: see text] and [Formula: see text], respectively. The corona product of the graphs [Formula: see text] and [Formula: see text], denoted by [Formula: see text], is constructed by taking one copy of [Formula: see text] and [Formula: see text] copies of [Formula: see text], connecting each vertex of the [Formula: see text]th copy of [Formula: see text] to the [Formula: see text]th vertex of [Formula: see text] by an edge. For any integer [Formula: see text], we recursively define the graph [Formula: see text] as [Formula: see text]. We present several results on the fault-tolerant metric dimension and the adjacency fault-tolerant resolving set of corona product graphs. Additionally, we explore the relationship between the fault-tolerant metric dimension and the adjacency fault-tolerant metric dimension of a graph [Formula: see text]. Finally, we determine the adjacency fault-tolerant metric dimension of path, cycle, complete, complete bipartite, and star graphs.