Enumeration of Rooted Cubic Planar Maps

Abstract. Although much work has been done on enumerating rooted planar maps since Tutte's pioneering works in early 1960s, many classes of maps with no loops or multiple edges are still untreated. In this paper, we enumerate three classes of cubic planar maps with no loops or multiple edges: 1-connected; 2-connected; 3-connected and triangle-free.