Document Type

Journal Article

Department/Unit

Department of Mathematics

Title

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

Language

English

Abstract

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. © 2013 Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag Berlin Heidelberg.

Keywords

L(j, k)-labeling, product of a path and a cycle

Publication Date

2013

Source Publication Title

Acta Mathematica Sinica, English Series

Volume

29

Issue

8

Start Page

1437

End Page

1448

Publisher

Springer Verlag

DOI

10.1007/s10114-013-2021-7

Link to Publisher's Edition

http://dx.doi.org/10.1007/s10114-013-2021-7

ISSN (print)

14398516

ISSN (electronic)

14397617

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