Distance spectral radius of digraphs with given connectivity

Let D ( G ⃗ ) denote the distance matrix of a strongly connected digraph G ⃗ . The largest eigenvalue of D ( G ⃗ ) is called the distance spectral radius of a digraph G ⃗ , denoted by ϱ ( G ⃗ ) . Recently, many studies proposed the use of ϱ ( G ⃗ ) as a molecular structure description of alkanes. In this paper, we characterize the extremal digraphs with minimum distance spectral radius among all digraphs with given vertex connectivity and the extremal graphs with minimum distance spectral radius among all graphs with given edge connectivity. Moreover, we give the exact value of the distance spectral radius of those extremal digraphs and graphs. We also characterize the graphs with the maximum distance spectral radius among all graphs of fixed order with given vertex connectivity 1 and 2.