Fault-Tolerant Metric Dimension of Barycentric Subdivision of Cayley Graphs

Abstract

Metric dimension and fault-tolerant metric dimension of any graph G is subject to size of resolving set. It has become more important in modern GPS and sensors based world as resolving set ensures that in case of semi outage system is still scalable using redundant interfaces. Metric dimension of several interesting classes of graphs have been investigated like Cayley digraphs, Cartesian product of graphs, wheel graphs, convex polytopes and certain networks for categorical product of graphs. In this paper we used the phenomena of barycentric subdivision of graph and proved that fault-tolerant metric dimension of barycentric subdivision of Cayley graph is constant.