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.