  The relative Cayley graph of a group $G$ with respect to its proper subgroup
$H$, is a graph whose vertices are elements of $G$ and two vertices $h\in H$
and $g\in G$ are adjacent if $g=hc$ for some $c\in C$, where $C$ is an
inversed-closed subset of $G$. We study the relative Cayley graphs and, among
other results, we discuss on their connectivity and forbidden structures, and
compute some of their important numerical invariants.
