Graph statistics of random trees
by
Patrick Bahls
University of North Carolina, Asheville
Coauthors: Samuel R. Kaplan

We investigate the expected distribution of vertex degrees and distances in families of trees constructed via the following random process, governed by a real-valued function f: (1) begin with an initial vertex, v₀; (2) after n ≥ 0 vertices have been created, append a new vertex, v_n, by attaching it to an existing vertex v_i chosen with probability proportional to f(d(v_i)). We focus our attention on the cases f(x) = x^a, a ≤ 1, generalizing a construction considered by T.F. Móri.

Date received: March 26, 2008