International Journal of Mathematics and Mathematical Sciences
Volume 19 (1996), Issue 2, Pages 411-414

On the basis of the direct product of paths and wheels

A. A. Al-Rhayyel

Department of Mathematics, Yarmouk University, Irbid, Jordan

Received 24 February 1994; Revised 22 March 1995

Copyright © 1996 A. A. Al-Rhayyel. 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.


The basis number, b(G), of a graph G is defined to be the least integer k such that G has a k-fold basis for its cycle space. In this paper we determine the basis number of the direct product of paths and wheels. It is proved that P2Wn,is planar, and b(PmWn)=3, for all m3 and n4.