1. Ordering trees by their distance spectral radii.
- Author
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Lin, Wenshui, Zhang, Yuan, Chen, Qi’an, Chen, Jiwen, Ma, Chi, and Chen, Junjie
- Subjects
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SPECTRAL theory , *MATRICES (Mathematics) , *GRAPH connectivity , *RADIUS (Geometry) , *EIGENVALUES , *MATHEMATICAL transformations , *UNIQUENESS (Mathematics) , *GEOMETRIC vertices - Abstract
Let D ( G ) be the distance matrix of a connected graph G . The distance spectral radius of G , denoted by ∂ 1 ( G ) , is the largest eigenvalue of D ( G ) . In this paper we present a new transformation of a certain graph G that decreases ∂ 1 ( G ) . With the transformation, we partially confirm a conjecture proposed by Stevanović and Ilić [17] by showing that, if Δ ≥ ⌈ n 2 ⌉ , the double star S Δ , n − Δ uniquely minimizes the distance spectral radius among all trees on n vertices with maximum degree Δ . Moreover, the trees on n ≥ 10 vertices with the fourth and fifth least distance spectral radii are characterized. [ABSTRACT FROM AUTHOR]
- Published
- 2016
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