TY - JOUR

T1 - L(j, k)-number of direct product of path and cycle

AU - SHIU, Wai Chee

AU - Wu, Qiong

N1 - Funding Information:
Received January 17, 2012, revised August 17, 2012, accepted October 19, 2012 Supported by Faculty Research Grant, Hong Kong Baptist University

PY - 2013/8

Y1 - 2013/8

N2 - 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 {pipe}f(u) - f(v){pipe} ≥ j if uv ∈ E(G), and {pipe}f(u) - f(v){pipe} ≥ k if d(u, v) = 2. Then the span of f is the difference between the maximum and the minimum numbers assigned by f. The L(j, k)-number of G, denoted by λj,k(G), is the minimum span over all L(j, k)-labelings of G. In this paper, we give some results about the L(j, k)-number of the direct product of a path and a cycle for j ≤ k.

AB - 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 {pipe}f(u) - f(v){pipe} ≥ j if uv ∈ E(G), and {pipe}f(u) - f(v){pipe} ≥ k if d(u, v) = 2. Then the span of f is the difference between the maximum and the minimum numbers assigned by f. The L(j, k)-number of G, denoted by λj,k(G), is the minimum span over all L(j, k)-labelings of G. In this paper, we give some results about the L(j, k)-number of the direct product of a path and a cycle for j ≤ k.

KW - L(j, k)-labeling

KW - product of a path and a cycle

UR - http://www.scopus.com/inward/record.url?scp=84880081748&partnerID=8YFLogxK

U2 - 10.1007/s10114-013-2021-7

DO - 10.1007/s10114-013-2021-7

M3 - Journal article

AN - SCOPUS:84880081748

SN - 1439-8516

VL - 29

SP - 1437

EP - 1448

JO - Acta Mathematica Sinica, English Series

JF - Acta Mathematica Sinica, English Series

IS - 8

ER -