2009/06/08 by Tuerker Biyikoglu, Biyikoglu, Tuerker, Josef Leydold +1
Computer Science · Mathematics · Physics and Astronomy · #05C05 #05C35 #05C50 #05C75 #Advanced Chemical Physics Studies #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications #Matrix Theory and Algorithms #Spectral Theory (math.SP) #math.CO #math.SP #msc:05C05 #msc:05C35 #msc:05C50 #msc:05C75
paper · pdf · doi:10.48550/arxiv.0906.1517
8 pages
arxiv created 2009/06/08 · openalex publication_date 2009/06/08 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A semiregular tree is a tree where all non-pendant vertices have the same degree. Belardo et al. (MATCH Commun. Math. Chem. 61(2), pp. 503-515, 2009) have shown that among all semiregular trees with a fixed order and degree, a graph with index is a caterpillar. In this technical report we provide a different proof for this theorem. Furthermore, we give counter examples that show this result cannot be generalized to the class of trees with a given (non-constant) degree sequence.