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arXiv · 1707.05083

Eigenvalues and Wiener index of the Zero Divisor graph $Γ[\mathbb {Z}_n]$

B. Surendranath Reddy·Rupali. S. Jain·N. Laxmikanth
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Abstract

The Zero divisor Graph of a commutative ring $R$, denoted by $Γ[R]$, is a graph whose vertices are non-zero zero divisors of $R$ and two vertices are adjacent if their product is zero. In this paper, we consider the zero divisor graph $Γ[\mathbb{Z}_n]$ for $n=p^3$ and $n=p^2q$ with $p$ and $q$ primes. We discuss the adjacency matrix and eigenvalues of the zero divisor graph $Γ[\mathbb{Z}_n]$. We also calculate the energy of the graph $Γ[\mathbb{Z}_n]$.

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B. Surendranath Reddy, Rupali. S. Jain, N. Laxmikanth. 2017-07-17. Eigenvalues and Wiener index of the Zero Divisor graph $Γ[\mathbb {Z}_n]$. https://arxiv.org/abs/1707.05083

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