Geodesic
An Application of Catalan Numbers on Cayley Tree of Order 2: Single Polygon Counting
Bulletin of the Malaysian Mathematical Society, Tome 31 (2008) no. 2 Cet article a éte moissonné depuis la source Bulletin of the Malaysian Mathematical Society website

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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.
Classification : 82B20, 11B83. 
@article{BMMS_2008_31_2_a6,
     author = {C. H. Pah},
     title = {An {Application} of {Catalan} {Numbers} on {Cayley} {Tree} of {Order} 2: {Single} {Polygon} {Counting}},
     journal = {Bulletin of the Malaysian Mathematical Society},
     year = {2008},
     volume = {31},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/BMMS_2008_31_2_a6/}
}
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C. H. Pah. An Application of Catalan Numbers on Cayley Tree of Order 2: Single Polygon Counting. Bulletin of the Malaysian Mathematical Society, Tome 31 (2008) no. 2. http://geodesic.mathdoc.fr/item/BMMS_2008_31_2_a6/