# Variety of Rational Resolving Sets of Power of a Cycle

### Abstract

To discover the actual route and to determine the position of a vertex in the network, we need to select the landmarks by making certain local measurement at the smallest subsets of the nodes. Since each of these measurements are potentially quite costly, the objective here is to minimize the number of measurements which still discover the whole graph. A subset of vertices of a graph is called a rational resolving set of if for each pair there is a vertex such that , where denotes the mean of the distances from the vertex *s* to all those A rational resolving set denoted by set, having minimum cardinality is a rational metric basis and its cardinality is the lower number, denoted by . The maximum cardinality of a minimal set is called the upper number of , denoted by *.* In this paper varieties of minimal rational resolving sets of a graph are defined on the basis of its compliments, called the lower and upper , , , numbers and discussed their optimality in power of a cycle