On study of some bounds for fault-tolerant metric dimension and adjacency fault-tolerant resolving set of corona product graphs - Shahzad, Muhammad Asif; Ali, Nasir; Osman Abdallah, Suhad Ali; Abd El-Gawaad, N. S. (Discrete mathematics, algorithms, and applications, 2025)
In this paper, we investigate bounds for the fault-tolerant metric dimension and adjacency fault-tolerant resolving set of corona product graphs. Let Q and R be two graphs with orders m 1 and m 2 , respectively. The corona product of the graphs Q and R , denoted by Q ⊙ R , is constructed by taking one copy of Q and m 1 copies of R , connecting each vertex of the i th copy of R to the i th vertex of Q by an edge. For any integer k > 1 , we recursively define the graph Q ⊙ k R as Q ⊙ k R = ( Q ⊙ k − 1 R ) ⊙ R . 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 Q . Finally, we determine the adjacency fault-tolerant metric dimension of path, cycle, complete, complete bipartite, and star graphs.