  In this article we introduce and study the intersection graph of graded
ideals of graded rings. The intersection graph of $G-$graded ideals of a graded
ring $(R,G)$ is a simple graph, denoted by $Gr_G(R)$, whose vertices are the
nontrivial graded ideals and two ideals are adjacent if they are not trivially
intersected. We study graphical properties for these graphs such as
connectivity, regularity, completeness, domination numbers, and girth. These
intersection graphs for faithful, strong, and first strong gradings are also
discussed. In addition, we investigate intersection graphs of
$\mathbb{Z}_2-$graded idealization, and we deal with intersection graph of
graded ideals when the grading group is an ordered groups.
