Connectivity, diameter, independence number and the distance spectral radius of graphs

Abstract

© 2017 Elsevier Inc. The distance spectral radius of a graph is the largest eigenvalue of its distance matrix. X.L. Zhang (2012) [31] determined the n-vertex graphs of given diameter with the minimum distance spectral radius. In this paper, we generalize this result by characterizing the graphs of order n with given connectivity and diameter having minimum distance spectral radius. In addition, we determine the minimum distance spectral radius of graphs among the n-vertex graphs with given connectivity and independence number, and characterize the corresponding extremal graph, thus determining the minimum distance spectral radius of graphs among n-vertex graphs with given connectivity (resp. independence) number.