Department of Mathematics
For positive numbers j and k, an L(j, k)-labeling f of G is an assignment of numbers to vertices of G such that |f(u) − f(v)| ≥ j if d(u, v) = 1, and |f(u) − f(v)| ≥ k if d(u, v) = 2. The span of f is the difference between the maximum and the minimum numbers assigned by f. The L(j, k)-labeling number of G, denoted by λj,k(G), is the minimum span over all L(j, k)-labelings of G. In this article, we completely determine the L(j, k)-labeling number (2j ≤ k) of the Cartesian product of path and cycle.
L(j, k)L(j, k)-labeling, Cartesian product, Path Cycle
Source Publication Title
Journal of Combinatorial Optimization
Link to Publisher's Edition
Wu, Qiong, Wai Chee Shiu, and Pak Kiu Sun. "L(j,k)-labeling number of Cartesian product of path and cycle." Journal of Combinatorial Optimization 31.2 (2016): 604-634.