On L(h, k)-labeling index of inverse graphs associated with finite cyclic groups

Abstract

An L(h, k)-labeling of a graph G. (V, E) is a function f: V -> [0,8) such that the positive difference between labels of the neighbouring vertices is at least h and the positive difference between the vertices separated by a distance 2 is at least k. *e difference between the highest and lowest assigned values is the index of an L(h, k)-labeling. The minimum number for which the graph admits an L(h, k)-labeling is called the required possible index of L(h, k)-labeling of G, and it is denoted by lambda(h)(k) (G). In this paper, we obtain an upper bound for the index of the L(h, k)-labeling for an inverse graph associated with a finite cyclic group, and we also establish the fact that the upper bound is sharp. Finally, we investigate a relation between L(h, k)-labeling with radio labeling of an inverse graph associated with a finite cyclic group.