The Commuting Graph of the Quaternion Algebra over Residue Classes of Integers

Abstract

The commuting graph of an arbitrary ring \(R\), denoted by \(\Gamma(R)\), is the graph whose vertices are all non-central elements of \(R\), and two distinct vertices \(a\) and \(b\) are adjacent if and only if \(ab = ba\). In this paper, we investigate the connectivity, the diameter, the maximum degree and the minimum degree of the commuting graph of the quaternion algebra \(\mathbb{Z}_n[i, j, k]\).