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
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, , of a graph is defined to be the least integer such that
has a -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 ,is planar, and , for all and .