on intersection minimal ideal graph of a ring

For a ring $r$, the intersection minimal ideal graph, denoted by $ wedge(r) $, is a simple undirected graph whose vertices are proper non-zero (right) ideals of $r$ and any two distinct vertices $i_{1}$ and $i_{2}$ are adjacent if and only if $ i_{1} cap i_{2}$ is a minimal ideal of $r$. in this article, we explore connectedness, clique number, split character, planarity, independence number, domination number of $wedge(r)$.