On cozero divisor graphs of ring Zn

Articles in Press

Document Type : Original paper

Authors

1 Department of Mathematics, College of Sciences, University of Sharjah, UAE

2 Mathematical Sciences Department, College of Science, United Arab Emirates University, Al Ain 15551, Abu Dhabi, UAE

3 Department of Mathematics, Faculty of Science, Shahid Rajaee Teacher Training University, Tehran, 16785-163, I.R. Iran

Abstract

The cozero divisor graph Γ′(R) of a commutative ring R  is a simple graph with vertex set as non-zero zero divisor elements of R such that two distinct vertices x and y are adjacent  iff x∉Ry and y∉Rx, where xR is the ideal generated by x. In this article we find the spectra of Γ′(Zn) for n∈{q1q2,q1q2q3,q1n1q2}, where qi's are primes. As a consequence we obtain the bounds for the largest (smallest) eigenvalues, bounds for spread, rank and inertia of Γ′(Zq1n1q2) along with the determinant, inverse and square of trace of its quotient matrix. We present the extremal bounds for the energy of Γ′(Zn) for n=q1n1q2 and characterize the extremal graphs attaining them. We close article with conclusion for furtherance.

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References

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Communications in Combinatorics and Optimization

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Available Online from 20 July 2024

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