Energy of signed digraphs

In this paper we extend the concept of energy to signed digraphs and we obtain Coulson’s integral formula for energy of signed digraphs. We compute formulae for energies of signed directed cycles and we show that energy of non cycle balanced signed directed cycles increases monotonically with respect to the number of vertices. We extend the concept of non-complete extended pp sum (or briefly, NEPS) to signed digraphs. We construct infinite families of noncospectral equienergetic signed digraphs. Moreover, we extend McClelland’s inequality to signed digraphs and also obtain a sharp upper bound for the energy of a signed digraph in terms of the number of arcs. Some open problems are also given at the end.