Let R be a commutative ring with identity and Nil(R) be the set of nilpotent elements of R. The nil-graph of ideals of R is defined as the graph AG_N(R) whose vertex set is {I:(0)and there exists a non-trivial ideal such that and two distinct vertices and are adjacent if and only if . Here, we study conditions under which is complete or bipartite. Also, the independence number of is determined, where is a reduced ring. Finally, we classify Artinian rings whose nil-graphs of ideals have genus at most one.
such that 
and two distinct vertices 
and 
. Here, we study conditions under which 
is complete or bipartite. Also, the independence number of 
is a reduced ring. Finally, we classify Artinian rings whose nil-graphs of ideals have genus at most one.