An application of Catalan Numbers on Cayley tree of order 2: Single Polygon Counting - Pah, Chin Hee (School of Mathematical Sciences, Universiti Sains Malaysia, 2008)
Abstract. In this paper, we consider a problem on finding the number of different single connected component containing a fixed root for a given number of vertices on semi-infinite Cayley tree. The solution of this problem is the well known Catalan numbers. The result is then extended to the complete graph. Then, we gave a suitable estimate for the given problem.