On \(L(h,k)\)-labeling index of inverse graphs associated with finite cyclic groups
Summary: An \(L(h,k)\)-labeling of a graph \(G=(V,E)\) is a function \(f:V\longrightarrow [0,\infty)\) 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 \(L(h,k)\)-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 \(\lambda_k^h (G)\). 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.
scientific article; zbMATH DE number 7361858