Document Type

Journal Article

Department/Unit

Department of Mathematics

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 |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.

Publication Year

2016

Journal Title

Journal of Combinatorial Optimization

Volume number

31

Issue number

2

Publisher

Springer Verlag

First Page (page number)

604

Last Page (page number)

634

Referreed

1

DOI

10.1007/s10878-014-9775-4

ISSN (print)

15732886

Link to Publisher’s Edition

https://dx.doi.org/10.1007/s10878-014-9775-4

Keywords

L(j, k)L(j, k)-labeling, Cartesian product, Path Cycle

Included in

Mathematics Commons

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