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Abstract
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International Journal of Mathematics and Mathematical Sciences
Volume 19 (1996), Issue 2, Pages 411-414
doi:10.1155/S0161171296000580

On the basis of the direct product of paths and wheels

A.A. Al-Rhayyel

Department of Mathematics, Yarmouk University, Irbid, Jordan

Abstract

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 P2∧Wn,is planar, and b(Pm∧Wn)=3, for all m≥3 and n≥4.