On The Skew Energy of Oriented Unicyclic Digraphs

The concept of the skew energy of a digraph was introduced by Adiga, Balakrishnan and \(S_0\) in \(2010\). Let \(\overrightarrow{G}\) be an oriented graph of order \(n\) and \(\lambda_1, \lambda_2, \dots, \lambda_n\) denote all the eigenvalues of the skew-adjacency matrix of \(\overrightarrow{G}\). The skew energy \(\varepsilon_s(\overrightarrow{G}) = \sum\limits_{i=1}^{n} |\lambda_i|\). Hou, Shen and Zhang determined the minimal and the second minimal skew energy of the oriented unicyclic graphs. In this paper, the oriented unicyclic graphs with the third, fourth and fifth minimal skew energy are characterized, respectively.