A note on distance spectral radius of trees

Wang, Yanna; Xing, Rundan; Zhou, Bo; Dong, Fengming

doi:10.1515/spma-2017-0021

Cited by 2 publications

(1 citation statement)

References 10 publications

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“…There is a survey of Aouchiche and Hansen [1] in 2014 on the relevant background and results on the spectrum of the distance matrix of a graph, and especially on the distance spectral radius. The extremal results on the distance spectral radius of trees may be found in [12,20] with fixed matching number, in [20,21] with given number of leaves, in [15,17,18,24] with given maximum degree, in [6,28] with fixed diameter, in [14] with fixed number of odd vertices, in [25] with fixed domination number, in [16] with given number of vertices of degree two, in [5] with fixed degree sequence, and in [15,16,26,27] for some particular classes of trees.…”

Section: Problems and Existing Resultsmentioning

confidence: 99%

Distance spectral radius of series-reduced trees with parameters

Deng

Lin

et al. 2021

RAIRO-Oper. Res.

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For a connected graph $G$, the distance matrix is a real-symmetric matrix where the $(u,v)$-entry is the distance between vertex $u$ and vertex $v$ in $G$. The distance spectral radius of $G$ is the largest eigenvalue of the distance matrix. A series-reduced tree is a tree with at least one internal vertex and all internal vertices having degree at least three. Those series-reduced trees that maximize the distance spectral radius are determined over all series-reduced trees with fixed order and maximum degree and over all series-reduced trees with fixed order and domination number, respectively.

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Section: Problems and Existing Resultsmentioning

confidence: 99%

Distance spectral radius of series-reduced trees with parameters

Deng

Lin

et al. 2021

RAIRO-Oper. Res.

Self Cite

View full text Add to dashboard Cite

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On the distance spectral radius of trees with given degree sequence

Dadedzi¹,

Misanantenaina²,

Wagner³

2020

Discuss. Math. Graph Theory

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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.

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A note on distance spectral radius of trees

Abstract: Abstract:The distance spectral radius of a connected graph is the largest eigenvalue of its distance matrix. We determine the unique non-starlike non-caterpillar tree with maximal distance spectral radius.

Cited by 2 publications

References 10 publications

Distance spectral radius of series-reduced trees with parameters

Distance spectral radius of series-reduced trees with parameters

On the distance spectral radius of trees with given degree sequence

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