Fault-Tolerant Resolvability in Some Classes of Line Graphs

Xuan Guo, Muhammad Faheem, Zohaib Zahid, Waqas Nazeer and Jingjng Li

Mathematical Problems in Engineering, 2020, vol. 2020, 1-8

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).

Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlmpe:1436872

DOI: 10.1155/2020/1436872

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