Eccentric Connectivity Index of Cartesian product and Strong product of Strongly Connected Digraphs

Let $G=(V,E)$ be a graph. The \emph{eccentric connectivity index} of $G$ is defined as $$ξ^C(G)=\sum_{u\in V(G)}d_uecc(u)$$ where $d_u$ and $ecc(u)$ are the degree and eccentricity of $u$, respectively. For a strongly connected digraph $D=(V,A)$, the eccentric connectivity index is defined as $$ξ^C(