Vol. 8, No. 5, 2015

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

Matthew Young

Vol. 8 (2015), No. 5, 753–761

We study adjacency matrices of zero-divisor graphs of 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 = p3, where p is a prime number. We also find upper and lower bounds for the largest eigenvalue for all n.

adjacency matrix, zero-divisor graph
Mathematical Subject Classification 2010
Primary: 05C50, 13M99
Received: 7 February 2014
Revised: 27 August 2014
Accepted: 19 September 2014
Published: 28 September 2015

Communicated by Kenneth S. Berenhaut
Matthew Young
Mathematics Department
Penn State University
University Park
008 McAllister Building
State College, PA 16802
United States