Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8902773 | AKCE International Journal of Graphs and Combinatorics | 2017 | 10 Pages |
Abstract
For jâ¤k, the L(j,k)-labeling arose from code assignment problem. That is, let j, k and m be positive numbers, an m-L(j,k)-labeling of a graph G is a mapping f:V(G)â[0,m] such that |f(u)âf(v)|â¥j if d(u,v)=1, and |f(u)âf(v)|â¥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. The kth power Gk of an undirected graph G is the graph with the vertex set of G in which two vertices are adjacent when their distance in G is at most k. In this paper, the L(j,k)-labeling numbers of Pn2 are determined for jâ¤k.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Qiong Wu, Wai Chee Shiu,