On the girth of the annihilating-ideal graph of a commutative ring
محورهای موضوعی : History and biographyM. Ahrari 1 , Sh. A. Safari Sabet 2 , B. Amini 3
1 - Department of Mathematics, Islamic Azad University,
Central Tehran Branch, Tehran, Iran
2 - Department of Mathematics, Islamic Azad University, Central Tehran Branch, Tehran, Iran
3 - Department of Mathematics, College of Sciences, Shiraz University, Shiraz, Iran
کلید واژه: annihilating-ideal graph, star graph, bipartite graph, girth,
چکیده مقاله :
The annihilating-ideal graph of a commutative ring $R$ isdenoted by $AG(R)$, whose vertices are all nonzero ideals of $R$with nonzero annihilators and two distinct vertices $I$ and $J$are adjacent if and only if $IJ=0$. In this article, we completelycharacterize rings $R$ when $gr(AG(R))\neq 3$.
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