On the Line Graph of the Zero Divisor Graph for the Ring of Gaussian Integers Modulo n

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the zero-divisor graph of a module

let $r$ be a commutative ring with identity and $m$ an $r$-module. in this paper, we associate a graph to $m$, say ${gamma}({}_{r}m)$, such that when $m=r$, ${gamma}({}_{r}m)$ coincide with the zero-divisor graph of $r$. many well-known results by d.f. anderson and p.s. livingston have been generalized for ${gamma}({}_{r}m)$. we show that ${gamma}({}_{r}m)$ is connected with ${diam}({gamma}({}_...

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ژورنال

عنوان ژورنال: International Journal of Combinatorics

سال: 2012

ISSN: 1687-9163,1687-9171

DOI: 10.1155/2012/957284