The zero-divisor Cayley graph of the residue class ring $\left(Z_n, \oplus, \odot\right)$

Abstract

In this paper the notion of the zero-divisor Cayley graph $G\left(Z_n, D_0\right)$, where $\left(Z_n, \oplus, \odot\right)$ is the ring of residue classes modulo $n, n \geq 1$, an integer and $D_0$ is the set of nonzero zero-divisors, is introduced and it is shown that $G\left(Z_n, D_0\right)$ can be decomposed into components, if $n$ is a power of a single prime and it is connected, if $n$ is a product of more than one prime power.