On a variant of k-plane trees

Fidel Ochieng  Oduol; Isaac Owino Okoth; Fredrick Oluoch Nyamwala

doi:10.13069/jacodesmath.v12i3.329

Fidel Ochieng Oduol Moi University
Isaac Owino Okoth Maseno University
Fredrick Oluoch Nyamwala Moi University

DOI: https://doi.org/10.13069/jacodesmath.v12i3.329

Keywords: $k$-plane tree, $k_1$-plane tree, root degree, eldest child, youngest child, forest

Abstract

In this paper, we introduce a class of plane trees whose vertices receive labels from the set {1,2,...,k} such that the sum
of labels of adjacent vertices does not exceed k+1 and all vertices of label 1 are always on the left of all other vertices.
Using generating functions, we enumerate these trees by number of vertices and label of the root, root degree, label of the
eldest or youngest child of the root and forests.