# On Randić spectrum of zero divisor graphs of commutative ring $\mathbb{Z}_{n}$

Document Type : Original paper

Authors

1 University of Kashmir

2 Department of Mathematics, Hazratbal

3 Central University of Kashmir

Abstract

For a finite commutative ring $\mathbb{Z}_{n}$ with identity $1\neq 0$, the zero divisor graph $\Gamma(\mathbb{Z}_{n})$ is a simple connected graph having vertex set as the set of non-zero zero divisors, where two vertices $x$ and $y$ are adjacent if and only if $xy=0$. We find the Randi'c spectrum of the zero divisor graphs $\Gamma(\mathbb{Z}_{n})$, for various values of $n$ and characterize $n$ for which $\Gamma(\mathbb{Z}_{n})$ is Randi'c integral.

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