Adjacency matrices of zero-divisor graphs of integers modulo n

Young, Matthew

doi:10.2140/involve.2015.8.753

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Adjacency matrices of zero-divisor graphs of integers modulo $n$

Matthew Young

Vol. 8 (2015), No. 5, 753–761

DOI: 10.2140/involve.2015.8.753

Abstract

We study adjacency matrices of zero-divisor graphs of $ℤ_{n}$ for various $n$ . We find their determinant and rank for all $n$ , develop a method for finding nonzero eigenvalues, and use it to find all eigenvalues for the case $n = p^{3}$ , where $p$ is a prime number. We also find upper and lower bounds for the largest eigenvalue for all $n$ .

Keywords

adjacency matrix, zero-divisor graph

Mathematical Subject Classification 2010

Primary: 05C50, 13M99

Milestones

Received: 7 February 2014

Revised: 27 August 2014

Accepted: 19 September 2014

Published: 28 September 2015

Communicated by Kenneth S. Berenhaut

Authors

Matthew Young
Mathematics Department Penn State University University Park 008 McAllister Building State College, PA 16802 United States

Vol. 8, No. 5, 2015