a new notion of energy of digraphs

The eigenvalues of a digraph are the eigenvalues of its adjacency matrix. let z1(. . . zn be the eigenvalues of an n-vertex digraph d. here, we give a new notion of energy of digraphs defined by ep (d ) =∑^n k = 1| r (zk) 3 (zk) | , where r (zk) and s (zk) are real and imaginary parts of zk, respectively. we call it pp-energy of the digraph and compute the p-energy formulas for directed cycles. for n > 1 2 , it is shown that pp-energy of directed cycles increases monotonically with respect to their order. the unicyclic digraphs with smallest and largest p-energy are obtained and counter examples will be presented to show that the p-energy of a digraph does not possess increasing-property with respect to quasi-order relation over the set , where is the set of n-vertex digraphs with cycles of length . also, an upper bound for the p-energy is presented and give all digraphs which attain this bound.