Semiregular Trees with Minimal Index

Biyikoglu, Türker and Leydold, Josef (2009) Semiregular Trees with Minimal Index. Research Report Series / Department of Statistics and Mathematics, 86. Department of Statistics and Mathematics, WU Vienna University of Economics and Business, Vienna.


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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 caterpillar. In this technical report we provide a different proof for this theorem. Furthermore, we give counter examples that show that this result cannot be generalized to the class of trees with a given (non-constant) degree sequence.

Item Type: Paper
Keywords: adjacency matrix / eigenvectors / spectral radius / Perron vector / tree
Classification Codes: MSC 05C35, 05C75, 05C05, 05C50
Divisions: Departments > Finance, Accounting and Statistics > Statistics and Mathematics
Depositing User: Repository Administrator
Date Deposited: 08 Jun 2009 16:28
Last Modified: 22 Oct 2019 00:41


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