Fault-tolerant metric dimension of interconnection networks

S. Hayat, A. Khan, M.Y.H. Malik, M. Imran, M.K. Siddiqui
2020 IEEE Access  
A fixed interconnection parallel architecture is characterized by a graph, with vertices corresponding to processing nodes and edges representing communication links. An ordered set R of nodes in a graph G is said to be a resolving set of G if every node in G is uniquely determined by its vector of distances to the nodes in R. Each node in R can be thought of as the site for a sonar or loran station, and each node location must be uniquely determined by its distances to the sites in R. A
more » ... olerant resolving set R for which the failure of any single station at node location v in R leaves us with a set that still is a resolving set. The metric dimension (resp. fault-tolerant metric dimension) is the minimum cardinality of a resolving set (resp. fault-tolerant resolving set). In this article, we study the metric and fault-tolerant dimension of certain families of interconnection networks. In particular, we focus on the fault-tolerant metric dimension of the butterfly, the Benes and a family of honeycomb derived networks called the silicate networks. Our main results assert that three aforementioned families of interconnection have an unbounded fault-tolerant resolvability structures. We achieve that by determining certain maximal and minimal results on their fault-tolerant metric dimension. INDEX TERMS Graph theory, metric dimension, fault-tolerant metric dimension, NP-complete problems, interconnection networks. ASAD KHAN received the bachelor's degree in applied mathematics from Government College University Faisalabad (GCUF), Pakistan, in 2010, the master's degree in mathematical modeling and scientific computing from Air University Islamabad (AIU), Pakistan, in 2012, and the Ph.D. degree in image and video processing from the University of Science and Technology (USTC), in 2017. He is currently working as a Postdoctoral Fellow and a Teaching Instructor with Guangzhou University, Guangzhou, China. His research interests include image processing, computer vision, deep learning, computational photography, hyperspectral imaging, and wearable computing. He is an active reviewer of several top tier journals and the IEEE TRANSACTIONS, including but not limited to Nature (Springer),
doi:10.1109/access.2020.3014883 fatcat:27oprgfqmza7vcvpn7gejoezme