On skew Laplacian spectrum and energy of digraphs

We consider the skew Laplacian matrix of a digraph (G) over right arrow obtained by giving an arbitrary direction to the edges of a graph G having n vertices and m edges. With v(1), v(2),...,.n to be the skew Laplacian eigenvalues of (G) over right arrow, the skew Laplacian energy SLE((G) over right arrow) of (G) over right arrow is defined as SLE((G) over right arrow) = Sigma(n)(i=1) vertical bar v(i)vertical bar. In this paper, we analyze the effect of changing the orientation of an induced subdigraph on the skew Laplacian spectrum. We obtain bounds for the skew Laplacian energy SLE((G) over right arrow) in terms of various parameters associated with the digraph (G) over right arrow and the underlying graph G and we characterize the extremal digraphs attaining these bounds. We also show these bounds improve some known bounds for some families of digraphs. Further, we show the existence of some families of skew Laplacian equienergetic digraphs.