Spectra of the zero-divisor graph of finite rings

Krishnat D. Masalkar; Anil Khairnar; Anita Lande; Avinash Patil

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arXiv · 2106.15977

Spectra of the zero-divisor graph of finite rings

Krishnat D. Masalkar·Anil Khairnar·Anita Lande·Avinash Patil

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Abstract

The zero-divisor graph $\Gamma(R)$ of a ring $R$ is a graph with nonzero zero-divisors of $R$ as vertices and distinct vertices $x,y$ are adjacent if $xy=0$ or $yx=0$. We provide an equivalence relation on a ring $R$ and express $\Gamma(R)$ as a generalized join of graphs on equivalence classes of this relation. We determined the adjacency and Lapalcian spectra of $\Gamma(R)$ when $R$ is a finite semisimple ring.

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Krishnat D. Masalkar, Anil Khairnar, Anita Lande, Avinash Patil. 2021-06-30. Spectra of the zero-divisor graph of finite rings. https://arxiv.org/abs/2106.15977

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