Semiregular Trees with Minimal Index
Combinatorics
2009-06-09 v1 Spectral Theory
Abstract
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.
Keywords
Cite
@article{arxiv.0906.1517,
title = {Semiregular Trees with Minimal Index},
author = {Tuerker Biyikoglu and Josef Leydold},
journal= {arXiv preprint arXiv:0906.1517},
year = {2009}
}
Comments
8 pages