Distance spectral radius of digraphs with given connectivity

Let D([email protected]?) denote the distance matrix of a strongly connected digraph [email protected]?. The largest eigenvalue of D([email protected]?) is called the distance spectral radius of a digraph [email protected]?, denoted by @r([email protected]?). Recently, many studies proposed the use of @r([email protected]?) 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.

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