TY - JOUR T1 - GENERALIZATIONS OF THE ZERO-DIVISOR GRAPH AU - Mcclurkin, Grace AU - Anderson, David F. PY - 2020 DA - January DO - 10.24330/ieja.663079 JF - International Electronic Journal of Algebra JO - IEJA PB - Abdullah HARMANCI WT - DergiPark SN - 1306-6048 SP - 237 EP - 262 VL - 27 IS - 27 LA - en AB - Let $R$ be a commutative ring with $1 \neq 0$ and $Z(R)$ itsset of zero-divisors. The zero-divisor graph of $R$ is the (simple) graph $\Gamma(R)$ with vertices $Z(R) \setminus \{0\}$, and distinct vertices $x$ and $y$ are adjacent if and only if $xy = 0$. In this paper, we consider generalizations of $\Gamma(R)$ by modifying the vertices or adjacency relations of $\Gamma(R)$. In particular, we study the extended zero-divisor graph $\overline{\Gamma}(R)$, the annihilator graph $AG(R)$, and their analogs for ideal-based and congruence-based graphs. KW - Zero-divisor graph KW - commutative ring with identity CR - M. Afkhami, N. Hoseini and K. 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