On spectrum of the zero-divisor graph of matrix ring

Krishnat Masalkar; Anil Khairnar; Anita Lande; Lata Kadam

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arXiv · 2312.09934

On spectrum of the zero-divisor graph of matrix ring

Krishnat Masalkar·Anil Khairnar·Anita Lande·Lata Kadam

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Abstract

For a ring $R$, the zero-divisor graph is a simple graph $\Gamma(R)$ whose vertex set is the set of all non-zero zero-divisors in a ring $R$, and two distinct vertices $x$ and $y$ are adjacent if and only if $xy=0$ or $yx=0$ in $R$. By using Weyl's inequality we give bounds on eigenvalues of adjacency matrix of $\Gamma(M_2(F))$, where $M_2(F)$ is a $2 \times 2$ matrix ring over a finite field $F$.

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BibTeX RIS

Krishnat Masalkar, Anil Khairnar, Anita Lande, Lata Kadam. 2023-12-15. On spectrum of the zero-divisor graph of matrix ring. https://arxiv.org/abs/2312.09934

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