3-Regular digraphs with optimum skew energy

The skew energy of a digraph D is defined as the sum of the singular values of its skew adjacency matrix $S(D)$. In this paper, we first interpret the entries of the power of the skew adjacency matrix of a digraph in terms of the number of its walks and then focus on the question posed by Adiga et al. C. Adiga, R. Balakrishnan, Wasin So, The skew energy of a graph, Linear Algebra Appl. 432 (2010) 1825–1835] of determining all $3$-regular connected digraphs with optimum skew energy.