DMGT

ISSN 1234-3099 (print version)

ISSN 2083-5892 (electronic version)

https://doi.org/10.7151/dmgt

Discussiones Mathematicae Graph Theory

IMPACT FACTOR 2019: 0.755

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Discussiones Mathematicae Graph Theory

Article in press


Authors:

K. Dadedzi, V. Razanajatovo Misanantenaina, S. Wagner

Title:

On the distance spectral radius of trees with given degree sequence

Source:

Discussiones Mathematicae Graph Theory

Received: 2019-04-30, Revised: 2019-07-09, Accepted: 2019-07-18, https://doi.org/10.7151/dmgt.2271

Abstract:

We consider the problem of maximizing the distance spectral radius and a slight generalization thereof among all trees with some prescribed degree sequence. We prove in particular that the maximum of the distance spectral radius has to be attained by a caterpillar for any given degree sequence. The same holds true for the terminal distance matrix. Moreover, we consider a generalized version of the reverse distance matrix and also study its spectral radius for trees with given degree sequence. We prove that the spectral radius is always maximized by a greedy tree. This implies several corollaries, among them a ``reversed'' version of a conjecture of Stevanović and Ilić. Our results parallel similar theorems for the Wiener index and other invariants.

Keywords:

distance matrix, spectral radius, tree, degree sequence

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