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

Document Type : Research Paper


1 Department of Mathematics, Manonmaniam Sundaranar University Tirunelveli 627 012, Tamil Nadu, India.

2 Department of Mathematics, Gobi Arts and Science College Karattadipalayam Gobichettipalayam-638 453, Tamil Nadu, India


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 $n$.


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