In this paper, we study the genera of zero-divisor graphs with respect to ideals in finite rings.

Let R be a commutative ring with nonzero identity and let id="M2"> Z its set of zero divisors. The zero-divisor graph id="M3"> is the id="M4"> ? vertex id="M5"> V = ? , wh...

In this paper, we introduce the multiplicative zero-divisor graph of a multiplicative lattice and study Beck-like coloring of such graphs. Further, it is proved that for such graphs, the chromatic number and the clique number need not be equal. On the other hand, if a multiplicative lattice L is reduced, then the chromatic number and the clique number of the multiplicative zero-divisor graph of...