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All Journal Electronic Journal of Graph Theory and Applications (EJGTA)
T. A. Chishti
Department of Mathematics, University of Kashmir, Srinagar, Kashmir, India
Electrical & Electronics Engineering

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On normalized Laplacian spectrum of zero divisor graphs of commutative ring ℤn S. Pirzada; Bilal A. Rather; T. A. Chishti; U. Samee
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 9, No 2 (2021): Electronic Journal of Graph Theory and Applications
Publisher : GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/ejgta.2021.9.2.7

Abstract

For a finite commutative ring ℤn with identity 1 ≠ 0, the zero divisor graph Γ(ℤn) 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 normalized Laplacian spectrum of the zero divisor graphs Γ(ℤn) for various values of n and characterize n for which Γ(ℤn) is normalized Laplacian integral. We also obtain bounds for the sum of graph invariant Sβ*(G)-the sum of the β-th power of the non-zero normalized Laplacian eigenvalues of Γ(ℤn).
Co-Authors Bilal A. Rather S. Pirzada U. Samee