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

Author(s):

G. Gold Belsi , S. Kavitha *

Message:
Article Type:
Research/Original Article (دارای رتبه معتبر)
Abstract:
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

Language:
English
Published:
Journal of Algebraic Structures and Their Applications, Volume:10 Issue: 1, Winter-Spring 2023
Pages:
131 to 139
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