2018/06/11 by Audace A. V. Dossou-Olory, Dossou-Olory, Audace Amen Vioutou
Computer Science · Mathematics · Physics and Astronomy · #05C35 #05C62 #11A41 #11Y05 #Combinatorics (math.CO) #Complex Network Analysis Techniques #FOS: Mathematics #Graph theory and applications #Primary 05C05 #Topological and Geometric Data Analysis #secondary 05C30
paper · pdf · doi:10.48550/arxiv.1806.03995
openalex publication_date 2018/06/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Denote by pm the m-th prime number (p1=2,~p2=3,~p3=5,~ p4=7,~…). Let T be a rooted tree with branches T1,T2,…,Tr. The Matula number M(T) of T is pM(T1)⋅ pM(T2)⋅ … ⋅ pM(Tr), starting with M(K1)=1. This number was put forward half a century ago by the American mathematician David Matula. In this paper, we prove that the star (consisting of a root and leaves attached to it) and the binary caterpillar (a binary tree whose internal vertices form a path starting at the root) have the smallest and greatest Matula number, respectively, over all topological trees (rooted trees without vertices of outdegree 1) with a prescribed number of leaves -- the extreme values are also derived.