Distance spectral radius of trees with fixed maximum degree

By Dragan Stevanovic, Aleksandar Ilić. 2010

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C ‡ Abstract. Distance energy is a newly introduced molecular graph-based analog of the total �-electron energy, and it is defined as the sum of the absolute eigenvalues of the molecular distance matrix. For trees and unicyclic graphs, distance energy is equal to the doubled value of the distance spectral radius. In this paper, we introduce a general transformation that increases the distance spectral radius and provide an alternative proof that the path Pn has the maximal distance spectral radius among trees on n vertices. Among the trees with a fixed maximum degree �, we prove that the broom Bn,� (consisting of a star S�+1 and a path of length n � 1 attached to an arbitrary pendent vertex of the star) is the unique tree that maximizes the distance spectral radius, and conjecture the structure of a tree which minimizes the distance spectral radius. As a first step towards this conjecture, we characterize the starlike trees with the minimum distance spectral radius.

Subfields: Computational Theory and Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/195641d1b0aadc0739ed80c2d473a9aae55a352d

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In Computational Theory and Mathematics

In Geometry and Topology

Citations in the corpus

On Distance Spectral Radius and Distance Energy of Graphs (2011, background): “We also discuss upper bounds for the distance energy.”