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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References

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Communications in Combinatorics and Optimization
Volume 8, Issue 1
March 2023
Pages 103-113

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