Reachability Results in Plane Trees

Authors : Albert NYARİARO, Isaac Owino OKOTH

Pages : 75-88

Doi:10.33434/cams.936558

View : 16 | Download : 8

Publication Date : 2021-06-30

Article Type : Research Paper

Abstract :In this paper, we obtain closed formulas for the number of reachable vertices in labelled plane trees by paths lengths, sinks, leaf sinks, first children, left most path, non-first children, and non-leaves. Our counting objects are plane trees having their edges oriented from a vertex of lower label towards a vertex of higher label. For each statistic, we obtain the average number of reachable vertices. Moreover, we obtain a counting formula for the number of plane trees on $n$ vertices such that exactly $k\leq n$ are reachable from the root.
Keywords : Plane tree, Leaf, Sink