When essential annihilating-ideal graphs are bipartite?

The essential annihilating-ideal graph $mathcal{EG}(R)$ of a commutative unital ring $R$ is a simple graph whose vertices are non-zero annihilating ideals of $R$ and there exists an edge between two distinct vertices $I,J$ if and only if $Ann(IJ)$ is an essential ideal of $R$. In this talk, the structures of all rings whose essential annihilating-ideal graphs are bipartite are characterized.