Sharp bounds on distance spectral radius of graphs

Abstract

Let D(G) denote the distance matrix of a connected graph G. The largest eigenvalue of D(G) is called the distance spectral radius of a graph G, denoted by ϱ(G). In this article, we give sharp upper and lower bounds for the distance spectral radius and characterize those graphs for which these bounds are best possible.

Keywords:

• distance spectral radius
• average distance degree
• pseudo distance regular

AMS Subject Classification:

• 05C50

View correction statement:

Sharp bounds on distance spectral radius of graphs

Acknowledgements

The authors are grateful to the referees and the editors for their valuable comments, corrections and suggestions which led to considerable improvements in presentation. Supported by the National Natural Science Foundation of China (Nos 11071078, 11075057).