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http://dx.doi.org/10.11568/kjm.2021.29.1.13

ON SIGNLESS LAPLACIAN SPECTRUM OF THE ZERO DIVISOR GRAPHS OF THE RING ℤn  

Pirzada, S. (Department of Mathematics, University of Kashmir)
Rather, Bilal A. (Department of Mathematics, University of Kashmir)
Shaban, Rezwan Ul (Department of Mathematics, University of Kashmir)
Merajuddin, Merajuddin (Department of Applied Mathematics, Aligarh Muslim University)
Publication Information
Korean Journal of Mathematics / v.29, no.1, 2021 , pp. 13-24 More about this Journal
Abstract
For a finite commutative ring R with identity 1 ≠ 0, the zero divisor graph ��(R) is a simple connected graph having vertex set as the set of nonzero zero divisors of R, where two vertices x and y are adjacent if and only if xy = 0. We find the signless Laplacian spectrum of the zero divisor graphs ��(ℤn) for various values of n. Also, we find signless Laplacian spectrum of ��(ℤn) for n = pz, z ≥ 2, in terms of signless Laplacian spectrum of its components and zeros of the characteristic polynomial of an auxiliary matrix. Further, we characterise n for which zero divisor graph ��(ℤn) are signless Laplacian integral.
Keywords
Signless Laplacian matrix; zero divisor graph; finite commutative ring;
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