Laplacian eigenvalues of the zero divisor graph of the ringZn
By Sriparna Chattopadhyay, K. Patra, B. K. Sahoo. Linear Algebra and its Applications, 2020
82 citations recorded by the source corpus.
Abstract We study the Laplacian eigenvalues of the zero divisor graph Γ ( Z n ) of the ring Z n and prove that Γ ( Z p t ) is Laplacian integral for every prime p and positive integer t ≥ 2 . We also prove that the Laplacian spectral radius and the algebraic connectivity of Γ ( Z n ) for most of the values of n are, respectively, the largest and the second smallest eigenvalues of the vertex weighted Laplacian matrix of a graph which is defined on the set of proper divisors of n. The values of n for which algebraic connectivity and vertex connectivity of Γ ( Z n ) coincide are also characterized.
Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/6d1241e791e4131c6de2bca0e1b36aff1c8a9563
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In Algebra and Number Theory
In Discrete Mathematics and Combinatorics
In Geometry and Topology
Citations in the corpus
- On Laplacian Eigenvalues of the Zero-Divisor Graph Associated to the Ring of Integers Modulo n (2021, methodology): “Evidently, this graph is a connected graph [5].”