Generation of Symmetric and Asymmetric Biconnected Rooted Outerplanar Graphs

In a rooted graph, a vertex is designated as its root. An outerplanar graph is represented by a plane embedding such that all vertices appear along its outer boundary. Two different plane embeddings of a rooted outerplanar graphs are called symmetric copies. Given integers n ≥ 3 and g ≥ 3, we give an O(n)-space and O(1)-time delay algorithm that enumerates all biconnected rooted outerplanar graphs with exactly n vertices such that the size of each inner face is at most g without delivering two symmetric copies of the same graph.