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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

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Official URL: http://math.usm.my/bulletin/pdf/v31n2/v31n2p7.pdf

Affiliations

International Islamic University Malaysia. Faculty of Science. Dept. of Computational and Theoretical Sciences

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.

Item Type:Journal
Keywords:Cayley tree, phase transition, contour method, Catalan numbers
Subjects:Q Science, Computer Science
ID Code:3968

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