On the Basis Number of the Wreath Product of Ladders

Abstract

The basis number of a graph \(G\) is defined to be the least non-negative integer \(d\) such that there is a basis \(\mathcal{B}\) of the cycle space of \(G\) such that each edge of \(G\) is contained in at most \(d\) members of \(\mathcal{B}\). In this paper, we determine the basis number of the wreath product of different ladders.