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The Scientific World Journal
Volume 2014 (2014), Article ID 741932, 12 pages
Research Article

-Labeling of the Strong Product of Paths and Cycles

1School of Information Science and Technology, Chengdu University, Chengdu 610106, China
2Key Laboratory of Pattern Recognition and Intelligent Information Processing, Institutions of Higher Education of Sichuan Province, Sichuan 610106, China
3Faculty of Natural Sciences and Mathematics, University of Maribor, Koroška Cesta 160, 2000 Maribor, Slovenia

Received 21 September 2013; Accepted 24 October 2013; Published 24 February 2014

Academic Editors: Y. Wang and S. Xiang

Copyright © 2014 Zehui Shao and Aleksander Vesel. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


An -labeling of a graph is a function from the vertex set to the set of nonnegative integers such that the labels on adjacent vertices differ by at least two and the labels on vertices at distance two differ by at least one. The span of is the difference between the largest and the smallest numbers in . The -number of , denoted by , is the minimum span over all -labelings of . We consider the -number of and for the -number of . We determine -numbers of graphs of interest with the exception of a finite number of graphs and we improve the bounds on the -number of , and .