Commutative rings with genus two annihilator graphs. Issue 1 (2nd January 2018) - Selvakumar, K.; Subajini, M.
ABSTRACT: Let R be a commutative ring and Z ( R )* be its set of all nonzero zero-divisors. The annihilator graph of a commutative ring R is the simple undirected graph AG ( R ) with vertices Z ( R )*, and two distinct vertices x and y are adjacent if and only if ann ( xy )≠ ann ( x )∪ ann ( y ). The notion of annihilator graph has been introduced and studied by Badawi [8 ]. In this paper, we classify the finite commutative rings whose AG ( R ) are projective. Also we determine all isomorphism classes of finite commutative rings with identity whose AG ( R ) has genus two.