ON THE HIGHER ORDER GENUS OF THE NILPOTENT GRAPH OF A RING.

For a commutative ring R, let Z_N(R)* = {x ∈ R: xy ∈ N(R) for some y ∈ R*}, which is the vertex set of the nilpotent graph Γ_N(R) and any two vertices x and y are adjacent if and only if xy ∈ N(R), where N(R) is the set of all nilpotent elements of R. In this article we discuss the higher order(two and three) genus of Γ_N(R). [ABSTRACT FROM AUTHOR]