On Lh,k-Labeling Index of Inverse Graphs Associated with Finite Cyclic Groups

Abstract

An Lh,k-labeling of a graph G=V,E is a function f:V⟶0,∞ 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. The difference between the highest and lowest assigned values is the index of an Lh,k-labeling. The minimum number for which the graph admits an Lh,k-labeling is called the required possible index of Lh,k-labeling of G, and it is denoted by λkhG. In this paper, we obtain an upper bound for the index of the Lh,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 Lh,k-labeling with radio labeling of an inverse graph associated with a finite cyclic group.