TITLE:
L(h, k)-Labeling of Circulant Graphs
AUTHORS:
Sarbari Mitra, Soumya Bhoumik
KEYWORDS:
Channel Assignment, L(h, k)-Labeling, Circulants, Connection Set
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.11 No.5,
May
31,
2023
ABSTRACT: An L(h,k)-labeling of a graph G is an assignment of non-negative integers to the vertices such that if two vertices u and v are adjacent then they receive labels that differ by at least h, and when u and v are not adjacent but there is a two-hop path between them, then they receive labels that differ by at least k. The span λ of such a labeling is the difference between the largest and the smallest vertex labels assigned. Let λhk (G)denote the least λ such that G admits an L(h,k) -labeling using labels from {0,1,...λ}. A Cayley graph of group is called circulant graph of order n, if the group is isomorphic to Zn. In this paper, initially we investigate the L(h,k) -labeling for circulant graphs with “large” connection sets, and then we extend our observation and find the span of L(h,k) -labeling for any circulants of order n.