Diameter of the commutativity graph of the real sedenions

Abstract

The commutativity graph of the real sedenion algebra is considered. It is shown that those elements whose imaginary part is not a zero divisor correspond to isolated vertices of this graph. All other elements form a connected component whose diameter equals $3$.

References in corpus (5)

• The zero divisors of the Cayley-Dickson algebras over the real numbers
• Constructing zero divisors in the higher dimensional Cayley-Dickson algebras
• Relation graphs of the sedenion algebra
• Orthogonality graphs of real Cayley-Dickson algebras. Part I: Doubly alternative zero divisors and their hexagons
• On doubly alternative zero divisors in Cayley-Dickson algebras