Connectivity and minimal distance spectral radius of graphs

Abstract

In this article, we study how the distance spectral radius behaves when the graph is perturbed by grafting edges. As applications, we also determine the graph with k cut vertices (respectively, k cut edges) with the minimal distance spectral radius.

Keywords:

• distance spectral radius
• pendant path

AMS Subject Classifications:

• 05C50
• 15A18

Acknowledgments

This article was finished when the author X. Zhang was a visiting PhD student in the Department of Combinatorics and Optimisation at the University of Waterloo from September 2008 to September 2009. X. Zhang is partially supported by NSFC grant no. 10831001.