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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)
  • Received : 2020.02.13
  • Accepted : 2021.01.12
  • Published : 2021.03.30

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

References

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