An application of Catalan Numbers on Cayley tree of order 2: Single Polygon Counting
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 complet...
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| Format: | Article |
| Language: | English |
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School of Mathematical Sciences, Universiti Sains Malaysia
2008
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| Online Access: | http://irep.iium.edu.my/297/ http://irep.iium.edu.my/297/ http://irep.iium.edu.my/297/1/v31n2p7.pdf |
| Summary: | 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. |
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