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

An - labeling of a graph is a function such that the positive difference between labels of the neighbouring vertices is at least and the positive difference between the vertices separated by a distance 2 is at least . The difference between the highest and lowest assigned values is the index of an - labeling. The minimum number for which the graph admits an - labeling is called the required possible index of - labeling of , and it is denoted by . In this paper, we obtain an upper bound for the index of the - 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 - labeling with radio labeling of an inverse graph associated with a finite cyclic group.