On the distance spectral radius of trees

Abstract

In this article, we prove that among trees on n vertices and matching number m, the dumbbell is the unique tree that maximizes the distance spectral radius, which was conjectured by Aleksandar Ilić [Distance spectral radius of trees with given matching number, Discr. Appl. Math. 158 (2010), pp. 1799–1806]. In addition, we find the unique tree that maximizes the distance spectral radius in the class of trees with a given number of pendent vertices.

Keywords:

• distance matrix
• distance spectral radius
• matching number

AMS Subject Classifications::

• 05C50
• 05C12

Acknowledgements

The authors sincerely thank the referees for their valuable comments and suggestions. The authors also thank the editors for some valuable suggestions that have improved this manuscript. The financial assistance for S. Paul was provided by DST, India, through INSPIRE Fellowship.