Counting Trees and Rooted Trees with Applications

J. C. Butcher ()
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J. C. Butcher: The University of Auckland

A chapter in Recent Advances in Mathematical Sciences, 2016, pp 1-11 from Springer

Abstract: Abstract Trees are connected graphs with no cycles. Rooted trees have a specific vertex designated to be the root. The order of a tree is the number of vertices. As the order increases the total number of trees or rooted trees with this order grows rapidly. A generating function for these totals will be demonstrated. The principal applications discussed in this talk are connected with the structures of Runge–Kutta methods and canonical Runge–Kutta methods.

Keywords: Trees; Rooted trees; Generating functions; Runge–Kutta methods; Order conditions; 65L05 (search for similar items in EconPapers)
Date: 2016
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-981-10-0519-0_1

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DOI: 10.1007/978-981-10-0519-0_1

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