  Let $G$ be a simple graph with $m$ edges and $H_i$, $1\leq i \leq m$ be
simple graphs too. The generalized edge corona product of graphs $G$ and $H_1,
..., H_m$, denoted by $G \diamond (H_1, ..., H_m)$, is obtained by taking one
copy of graphs $G$, $H_1, ..., H_m$ and joining two end vertices of $i$-th edge
of $G$ to every vertex of $H_i$, $1\leq i \leq m$. In this paper, some results
regarding the $k$-distance chromatic number of Generalized edge corona product
of graphs are presented. Also, as a consequence of our results, we compute this
invariant for the graphs $K_n \diamond (H_1, ..., H_m)$, $T\diamond (H_1, ...,
H_m)$ and $K_{m,n} \diamond (H_1, ..., H_m)$. Moreover, the domination set,
domination number and the independence number of any connected graph $G$ and
arbitrary graphs $H_i$, $1\leq i \leq |E(G)|$, are evaluated under generalized
edge corona operation.
