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.
Original language | English |
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Pages (from-to) | 495-524 |
Number of pages | 30 |
Journal | Discussiones Mathematicae - Graph Theory |
Volume | 40 |
Issue number | 2 |
DOIs | |
Publication status | Published - 1 May 2020 |
Externally published | Yes |
Keywords
- degree sequence
- distance matrix
- spectral radius
- tree