On normalized Laplacian spectrum of zero divisor graphs of commutative ring ℤn

S. Pirzada (Department of Mathematics, University of Kashmir, Srinagar, Kashmir, India)
Bilal A. Rather (Department of Mathematics, University of Kashmir, Srinagar, Kashmir, India)
T. A. Chishti (Department of Mathematics, University of Kashmir, Srinagar, Kashmir, India)
U. Samee (Department of Mathematics, University of Kashmir, Srinagar, Kashmir, India)

Electronic Journal of Graph Theory and Applications (EJGTA)
Vol 9, No 2 (2021): Electronic Journal of Graph Theory and Applications

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).