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. (C) 2011 Elsevier Inc. All rights reserved.