Enumeration of rooted nonseparable outerplanar maps

Abstract

In this paper, the number of combinatorially distinct rooted nonseparable outerplanar maps withm edges and the valency of the root-face beingn is found to be $$\frac{{(m - 1)!(m - 2)!}}{{(n - 1)!(n - 2)!(m - n)!(m - n + 1)!}}.$$ And, the number of rooted nonseparable outerplanar maps withm edges is also determined to be $$\frac{{(2m - 2)!}}{{(m - 1)!m!}},$$ which is just the number of distinct rooted plane trees withm − 1 edges.