  For $r\geq 1$, the $r$-independence complex of a graph $G$, denoted
Ind$_r(G)$, is a simplicial complex whose faces are subsets $A \subseteq V(G)$
such that each component of the induced subgraph $G[A]$ has at most $r$
vertices. In this article, we establish a relation between the distance
$r$-domination number of $G$ and (homological) connectivity of Ind$_r(G)$. We
also prove that Ind$_r(G)$, for a chordal graph $G$, is either contractible or
homotopy equivalent to a wedge of spheres. Given a wedge of spheres, we also
provide a construction of a chordal graph whose $r$-independence complex has
the homotopy type of the given wedge.
