5 citations · 15 across the 11 of their papers we have counts for
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Orthogonality graphs of real Cayley-Dickson algebras. Part I: Doubly alternative zero divisors and their hexagons
Svetlana Zhilina
We study zero divisors whose components alternate strongly pairwise and construct oriented hexagons in the zero divisor graph of an arbitrary real Cayley-Dickson algebra. In case o…
Orthogonality graphs of real Cayley-Dickson algebras. Part II: The subgraph on pairs of basis elements
Svetlana Zhilina
We consider zero divisors of an arbitrary real Cayley-Dickson algebra such that their components are both standard basis elements. We construct inductively the orthogonality graph…
Commuting graphs of Okubo algebras
Svetlana Zhilina, Danil Pavlinov
Commuting graphs of Okubo algebras are considered, and the problem of their connectivity is studied. The commuting graph of a pseudo-octonion algebra over a field…
Relation graphs of the sedenion algebra
Alexander Guterman, Svetlana Zhilina
Let denote the algebra of the sedenions, and denote its orthogonality graph. We observe that any pair of zero divisors in produces a dou…
On doubly alternative zero divisors in Cayley-Dickson algebras
Svetlana Zhilina
Zero divisors of Cayley-Dickson algebras over an arbitrary field , , are studied. It is shown that zero divisors, whose components a…
Diameter of the commutativity graph of the real sedenions
Svetlana Zhilina
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 th…