Geodesic
On the genus of the annihilator graph of a~commutative ring
Algebra and discrete mathematics, Tome 24 (2017) no. 2, pp. 191-208

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Let $R$ be a commutative ring and $Z(R)^*$ be its set of non-zero zero-divisors. The annihilator graph of a commutative ring $R$ is the simple undirected graph $\operatorname{AG}(R)$ with vertices $Z(R)^*$, and two distinct vertices $x$ and $y$ are adjacent if and only if $\operatorname{ann}(xy)\neq \operatorname{ann}(x)\cup \operatorname{ann}(y)$. The notion of annihilator graph has been introduced and studied by A. Badawi [7]. In this paper, we determine isomorphism classes of finite commutative rings with identity whose $\operatorname{AG}(R)$ has genus less or equal to one.
Keywords: commutative ring, annihilator graph, planar, local rings.
Mots-clés : genus 
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     author = {T. Tamizh Chelvam and K. Selvakumar},
     title = {On the genus of the annihilator graph of a~commutative ring},
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     url = {http://geodesic.mathdoc.fr/item/ADM_2017_24_2_a1/}
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T. Tamizh Chelvam; K. Selvakumar. On the genus of the annihilator graph of a~commutative ring. Algebra and discrete mathematics, Tome 24 (2017) no. 2, pp. 191-208. http://geodesic.mathdoc.fr/item/ADM_2017_24_2_a1/