TY - JOUR

T1 - L(j,k)-labeling numbers of square of paths

AU - Wu, Qiong

AU - SHIU, Wai Chee

N1 - Funding Information:
This work is supported by Tianjin Research Program of Application Foundation and Advanced Technology , Tianjin Municipal Science and Technology Commission , Faculty Research Grant of Hong Kong Baptist University .

PY - 2017/12

Y1 - 2017/12

N2 - For j≤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)→[0,m] 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. 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 j≤k.

AB - For j≤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)→[0,m] 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. 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 j≤k.

KW - Code assignment

KW - L(j,k)-labeling

KW - Path

KW - Square of path

UR - http://www.scopus.com/inward/record.url?scp=85029143593&partnerID=8YFLogxK

U2 - 10.1016/j.akcej.2017.07.001

DO - 10.1016/j.akcej.2017.07.001

M3 - Article

AN - SCOPUS:85029143593

VL - 14

SP - 307

EP - 316

JO - AKCE International Journal of Graphs and Combinatorics

JF - AKCE International Journal of Graphs and Combinatorics

SN - 0972-8600

IS - 3

ER -