A bipancyclic graph on \( v \) vertices is a bipartite graph that contains, as subgraphs, cycles of length \( n \) for every even integer \( n \) such that \( 4 \leq n \leq v \). Such a graph is uniquely bipancyclic if it contains exactly one subgraph of each permissible length.
In this paper, we find all uniquely bipancyclic graphs on 30 or fewer vertices.