Let $G=(V(G),E(G))$ be a digraph without loops and‎ ‎multiarcs‎, ‎where $V(G)={v_1,v_2,$ $ldots,v_n}$ and $E(G)$ are the‎ ‎vertex set and the arc set of $G$‎, ‎respectively‎. ‎Let $d_i^{+}$ be the‎ ‎outdegree of the vertex ...