## Abstract

Given a commutative ring R with identity 1≠0, let the set Z(R) denote the set of zero-divisors and let Z*(R)=Z(R)∖0 be the set of non-zero zero-divisors of R. The zero-divisor graph of R, denoted by Γ(R), is a simple graph whose vertex set is Z*(R) and each pair of vertices in Z*(R) are adjacent when their product is 0. In this article, we find the structure and Laplacian spectrum of the zero-divisor graphs Γ(Zn) for n=pN1qN2, where p<q are primes and N1,N2 are positive integers.

Original language | English |
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Article number | 482 |

Number of pages | 17 |

Journal | Mathematics |

Volume | 9 |

Issue number | 5 |

DOIs | |

Publication status | Published - 26 Feb 2021 |

## Keywords

- Eulers’s totient function
- Gaussian integer ring
- Integers modulo ring
- Laplacian matrix
- Zero-divisor graph

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