On the Neighbor-Determination in Cayley Graphs

Abstract

To determine the vertices of a connected graph through distance, many parameters are formed by varying the concept of metric generator in graph theory, such as connected metric generator, independent metric generator, doubly metric generator, strong metric generator, local metric generator and fault-tolerant metric generator to name a few. In this paper we determining every two neighbors in two families of Cayley graphs by investigating their local metric generator and fault-tolerant local metric generator.