(a) Show that the number of planted plane trees on n vertices, m of which are leaves (thatis, have zero upward branches) is )C).(b) Show that the average number of leaves in planted plane trees on n vertices is n/2.

To show that:a) The number of planted plane trees on vertices, of which are leaves (i.e. have zero…

Answered: a) Show that the number of planted…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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a) Show that the number of planted plane trees on n vertices, m of which are leaves (that is, have zero upward branches) is (m) (m-²). b) Show that the average number of leaves in planted plane trees on n vertices is n/2.