On the basis of the direct product of paths and wheels
Ahmad Al-Rhayyel · International Journal of Mathematics and Mathematical Sciences · 1995
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.