Upper and lower bounds of the basis number of Kronecker product of a wheel with a path and a cycle

Abstract EN

The basis number, b (G), of a graph G is defined to be the smallest positive integer k such that G has a k-fold basis for its cycle space.

We investigate upper and lower bounds of the basis number of Kronecker product of a wheel with a path and a cycle.

It is proved that 3 ≤ b (Wm ⊗ Pn) ≤ 4, m ≥ 4 and n ≥ 3, 3 ≤ b (Wm ⊗ Cn) ≤ 5, m ≥ 4, n ≥ 3.