Note on the exponential recursive k-ary trees

Abstract

In the present paper, we consider exponential recursive trees with no node of outdegree greater than k, called exponential recursive k-ary trees (k ≥ 2). At each step of growing of these trees, every external node (insertion position) is changed into a leaf with probability p, or fails to do so with probability 1 — p. We investigate limiting behavior of fundamental parameters such as size, leaves and distances in exponential recursive k-ary trees.