An Application of Catalan Numbers on Cayley Tree of Order 2: Single Polygon Counting
Pah, C.H., (2008) An Application of Catalan Numbers on Cayley Tree of Order 2: Single Polygon Counting. Bulletin of the Malaysian Mathematical Sciences Society, 31 (2). pp. 173-183. ISSN 0126-6705
Official URL: http://math.usm.my/bulletin/pdf/v31n2/v31n2p7.pdf
International Islamic University Malaysia. Faculty of Science. Dept. of Computational and Theoretical Sciences
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.
|Keywords:||Cayley tree, phase transition, contour method, Catalan numbers|
|Subjects:||Q Science, Computer Science|
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