Reachability in complete t-ary trees

Authors

  • Sylvester Arthur Abayo Department of Pure and Applied Mathematics, Maseno University, Kenya
  • Isaac Owino Okoth Maseno UniversityDepartment of Pure and Applied Mathematics, Maseno University, Kenya
  • Donnie Munyao Kasyoki Department of Pure and Applied Mathematics, Maseno University, Kenya

DOI:

https://doi.org/10.56947/amcs.v18.191

Keywords:

complete t-ary tree, path length, sink, leaf sink, leftmost path, first child, non-first child

Abstract

Mathematical trees such as Cayley trees, plane trees, binary trees, noncrossing trees, t-ary trees among others have been studied extensively. Reachability of vertices as a statistic has been studied in Cayley trees, plane trees, noncrossing trees and recently in t-ary trees where all edges are oriented from vertices of lower label towards vertices of higher label. In this paper, we obtain closed formulas as well as asymptotic formulas for the number of complete t-ary trees in which there are paths of a given length such that the terminal vertex is a sink, leaf sink, first child and non-first child. We also obtain number of trees in which there is a leftmost path of a given length.

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Published

2023-10-01

Issue

Section

Articles