- Communications in Advanced Mathematical Sciences
- Vol: 4 Issue: 2
- Reachability Results in Plane Trees
Reachability Results in Plane Trees
Authors : Albert Nyariaro, Isaac Owino Okoth
Pages : 75-88
Doi:10.33434/cams.936558
View : 12 | Download : 8
Publication Date : 2021-06-30
Article Type : Research
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