A Family of special outerplanar graphs with only one triangle satisfying the cycle basis interpolation property

The length of a cycle basis of a graph G is the sum of the lengths of its cycles. Let c−, c+ be the lengths of the minimal and maximal cycle basis, respectively. Then G has the cycle basis interpolation property (cbip) if for all integers c, c− < c < c+, there exists a cycle basis of length c. In this paper, we will prove that a family of special outerplanar graphs with only one triangle, namely bamboo shoot graphs, have the cbip.