  For a simple graph $G$, the $3$-distance graph, $D_3(G)$, is a graph with the
vertex set $V(G)$ and two vertices are adjacent if and only if their distance
is $3$ in the graph $G$. For a connected graph $G$, we provide some conditions
for the connectedness of $D_3(G)$. Also, we characterize all trees and
unicyclic graphs with connected $3$-distance graph.
