Reverse Wiener spectral radius of trees

Abstract

Let H be a connected graph with diameter μ and with distance matrix D. The reverse Wiener matrix of H is considered as $\mu (J-I)-D$, where I and J are the identity and all-ones matrix, respectively. The reverse Wiener spectral radius of H is the greatest eigenvalue of its reverse Wiener matrix. In this paper we obtain some relations on reverse Wiener spectral radius of graphs. We show that among all trees the paths have maximum and the stars have minimum reverse Wiener spectral radius.

Keywords:

• Reverse Wiener matrix
• reverse Wiener spectral radius

AMS Classification::

• 05C31
• 05C50
• 15A18

Acknowledgments

The author is grateful to the referee for helpful comments.

Disclosure statement

No potential conflict of interest was reported by the author(s).