THE ZERO-DIVISOR GRAPHS OF Z(+)Zn AND (Z(+)Zn)[X]]

초록

Let Z be the ring of integers and let Zn be the ring of integers modulo n. Let Z(+)Z(n) be the idealization of Zn in Z and let (Z(+)Z(n))[X]] be either (Z(+)Z(n))[X] or (Z(+)Z(n))[[X]]. In this article, we study the zerodivisor graphs of Z(+)Z(n) and (Z(+)Z(n))[X]]. More precisely, we completely characterize the diameter and the girth of the zero-divisor graphs of Z(+)Z(n) and (Z(+)Z(n))[X]]. We also calculate the chromatic number of the zerodivisor graphs of Z(+)Z(n) and (Z(+)Z(n))[X]].

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