Single Polygon Counting on Cayley Tree of Order 3
We showed that one form of generalized Catalan numbers is the solution to the problem of finding different connected component with finite vertices containing a fixed root for the semi-infinite Cayley tree of order 3. We give the formula for the full graph, Cayley tree of order 3 which is derived fr...
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| Format: | Article |
| Language: | English |
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Springer
2010
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| Online Access: | http://irep.iium.edu.my/293/ http://irep.iium.edu.my/293/ http://irep.iium.edu.my/293/ http://irep.iium.edu.my/293/1/Single_polygon_counting_on_cayley_tree_of_order_3_%281%29.pdf |
| Summary: | We showed that one form of generalized Catalan numbers is the solution to the problem of finding different connected component with finite vertices containing a fixed root for the semi-infinite Cayley tree of order 3. We give the formula for the full graph, Cayley tree of order 3 which is derived from the generalized Catalan numbers. Using ratios of Gamma functions, two upper bounds are given for problem defined on semi-infinite Cayley tree of order 3 as well as the full graph. |
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