Fault-Tolerant Resolvability in Some Classes of Line Graphs

الملخص EN

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).