Geodesic
Zero-Annihilator Graphs of Commutative Rings
Kragujevac Journal of Mathematics, Tome 42 (2018) no. 4, p. 517

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Assume that $R$ is a commutative ring with nonzero identity. In this paper, we introduce and investigate { zero-annihilator graph of} $R$ denoted by $\mathtt{ZA}(R)$. It is the graph whose vertex set is the set of all nonzero nonunit elements of $R$ and two distinct vertices $x$ and $y$ are adjacent whenever ${\rm Ann}_R(x)\cap {\rm Ann}_R(y)=\{0\}$.
Classification : 13A15 16N40
Keywords: Graphs, commutative rings, zero-annihilator graphs 
@article{KJM_2018_42_4_a3,
     author = {Hojjat Mostafanasab},
     title = {Zero-Annihilator {Graphs} of {Commutative} {Rings}},
     journal = {Kragujevac Journal of Mathematics},
     pages = {517 },
     publisher = {mathdoc},
     volume = {42},
     number = {4},
     year = {2018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KJM_2018_42_4_a3/}
}
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Hojjat Mostafanasab. Zero-Annihilator Graphs of Commutative Rings. Kragujevac Journal of Mathematics, Tome 42 (2018) no. 4, p. 517 . http://geodesic.mathdoc.fr/item/KJM_2018_42_4_a3/