Bounds for the signless Laplacian energy of digraphs

Let G be a digraph with n vertices, a arcs, c ₂ directed closed walks of length 2. Let q1; q2;:::; q _n be the eigenvalues of the signless Laplacian matrix of G. The signless Laplacian energy of a digraph G is defined as E _SL (G) = \(\sum\limits_{i = 1}^n {\left| {{q_i} - \frac{a}{n}} \right|} \). In this paper, some lower and upper bounds are derived for the signless Laplacian energy of digraphs.