Gordon-Scantlebury and Platt Indices of Random Plane-oriented Recursive Trees

Abstract

‎For a simple graph G‎, ‎the Gordon-Scantlebury index of G is equal to the number of paths of length two in G‎, ‎and the Platt index is equal to the total sum of the degrees of all edges in G‎. ‎In this paper‎, ‎we study these indices in random plane-oriented recursive trees through a recurrence equation for the first Zagreb index‎. ‎As n ∊ ∞, ‎the asymptotic normality of these indices are given‎.

Keywords

• gordon-scantlebury index‎
• ‎platt index‎
• ‎the first zagreb index‎
• plane-oriented recursive tree‎
• ‎asymptotic normality