On the skew spectral moments of graphs

Let G be a simple graph‎, ‎and G^{\sigma}‎ ‎be an oriented graph of G with the orientation ‎\sigma and skew-adjacency matrix S(G^{\sigma})‎. ‎The k-th skew spectral‎ ‎moment of G^{\sigma}‎, ‎denoted by‎ ‎T_k(G^{\sigma})‎, ‎is defined as \sum_{i=۱}^{n}( ‎‎‎\lambda_{i})^{k}‎, ‎where \lambda_{۱}‎, ‎\lambda_{۲},\cdots‎, ‎\lambda_{n} are the eigenvalues of G^{\sigma}‎. ‎Suppose‎ ‎G^{\sigma_۱}_{۱} and G^{\sigma_۲}_{۲} are two digraphs‎. ‎If there‎ ‎exists an integer k‎, ‎۱ \leq k \leq n-۱‎, ‎such that for each‎ ‎i‎, ‎۰ \leq i \leq k-۱‎, ‎T_i(G^{\sigma_۱}_{۱}) =‎ ‎T_i(G^{\sigma_۲}_{۲}) and‎ ‎T_k(G^{\sigma_۱}_{۱})