Fault-Tolerant Resolvability in Some Classes of Line Graphs. (26th September 2020)

• Record Type: Journal Article
• Authors: Guo, Xuan; Faheem, Muhammad; Zahid, Zohaib; Nazeer, Waqas; Li, Jingjng
• Other Names: Mourtzis Dimitris Academic Editor.
• Is Part Of: Mathematical problems in engineering. Volume 2020(2020)
• Publication Date: 2020-09-26
• Subjects: Engineering mathematics -- Periodicals; 510.2462
• DOI: 10.1155/2020/1436872
• Languages: English
• ISSNs: 1024-123X

Abstract

Abstract : Fault tolerance is the characteristic of a system that permits it to carry on its intended operations in case of the failure of one of its units. Such a system is known as the fault-tolerant self-stable system. In graph theory, if we remove any vertex in a resolving set, then the resulting set is also a resolving set, called the fault-tolerant resolving set, and its minimum cardinality is called the fault-tolerant metric dimension. In this paper, we determine the fault-tolerant resolvability in line graphs. As a main result, we computed the fault-tolerant metric dimension of line graphs of necklace and prism graphs (2010 Mathematics Subject Classification: 05C78).