On the basic properties of the Compressed annihilator graph of \mathbb{Z}_n

For a commutative ring R, the compressed annihilator graph AG_E(R) is defined by, taking the equivalence classes of zero divisors of R as the vertex set and two distinct vertices [a] and [b] are adjacent if and only if ann(a) \cup ann (b) \subset ann(ab). In this paper, we discuss some of the basic properties such as degree of the vertices, Eulerian, regularity, domination number and planarity of AG_E(\mathbb{Z}_n), where \mathbb{Z}_n is the ring of integer modulo n.

Keywords:

Compressed annihilator graph , Domination polynomial , Eulerian , Planarity