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

Author(s):

Bilal Rather , Shariefuddin Pirzada * , Imran Bhat , Tariq Chishti

Message:
Article Type:
Research/Original Article (دارای رتبه معتبر)
Abstract:
For a finite commutative ring $ mathbb{Z}_{n} $ with identity $ 1neq 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.
Keywords:

Randić matrix , Randić spectrum , zero divisor graph , Commutative rings

Language:
English
Published:
Communications in Combinatorics and Optimization, Volume:8 Issue: 1, Winter 2023
Pages:
103 to 113
https://www.magiran.com/p2493688