L(2,1)-labeling of circulant graphs
Soumya Bhoumik, Sarbari Mitra · Discussiones Mathematicae Graph Theory · 2018
An L(2, 1)-labeling of a graph is an assignment of non-negative integers to the vertices such that adjacent vertices receive labels that differ by at least 2, and those at a distance of two receive labels that differ by at least one. Let 1 2 () denote the least such that admits an L(2, 1)-labeling using labels from {0, 1, . . . , }. A Cayley graph of group G is called a circulant graph of order n, if G = Z n . In this paper initially we investigate the upper bound for the span of the L(2, 1)-labeling for Cayley graphs on cyclic groups with "large" connection sets. Then we extend our observation and find the span of L(2, 1)-labeling for any circulants of order n.