an:06644148
Zbl 1413.05172
Long, Shude; Cai, Junliang
Enumeration of a class of rooted planar unicyclic maps
EN
Ars Comb. 125, 47-62 (2016).
00360062
2016
j
05C30
unicyclic map; enumerating function; functional equation; Lagrangian inversion
Summary: A unicyclic map is a rooted planar map such that there is only one cycle which is the boundary of the unique inner face (the inner face contains no trees) and the root-vertex is on the cycle. In this paper we investigate the number of unicyclic maps and present some formulae for such maps with up to three parameters: the number of edges and the valencies of the root-vertex and the root-face.