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


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Mageshwaran K., Kalaimurugan G., Hammachukiattikul B., Govindan V., Cangül İ. N.

JOURNAL OF MATHEMATICS, vol.2021, 2021 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 2021
  • Publication Date: 2021
  • Doi Number: 10.1155/2021/5583433
  • Title of Journal : JOURNAL OF MATHEMATICS

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.