k-Protected Vertices in Unlabeled Rooted Plane Trees
نویسنده
چکیده
We find a simple, closed formula for the proportion of vertices which are k -protected in all unlabeled rooted plane trees on n vertices. We also find that, as n goes to infinity, the average rank of a random vertex in a tree of size n approaches 0.727649, and the average rank of the root of a tree of size n approaches 1.62297. Mathematics Subject Classification 05A15 · 05A16 · 05C05 tree, enumeration, asymptotics 2010 Mathematics Subject Classification. Primary: 05A15, 05C05; Secondary: 05A16. 1 2 KEITH COPENHAVER
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عنوان ژورنال:
- Graphs and Combinatorics
دوره 33 شماره
صفحات -
تاریخ انتشار 2017