On study of some bounds for fault-tolerant metric dimension and adjacency fault-tolerant resolving set of corona product graphs

• Published in: Discrete mathematics, algorithms, and applications Vol. 17; no. 7
• Main Authors: Shahzad, Muhammad Asif, Ali, Nasir, Osman Abdallah, Suhad Ali, Abd El-Gawaad, N. S.
• Format: Journal Article
• Language: English
• Published: Singapore World Scientific Publishing Company 01.10.2025; World Scientific Publishing Co. Pte., Ltd
• Subjects: Fault tolerance; Graphs; graphs; distance; Metric dimension; fault-tolerant metric dimension; resolving set
• ISSN: 1793-8309; 1793-8317
• DOI: 10.1142/S1793830924501052

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.