Graph theory and finite-dimensional alternative algebras

Abstract

In this paper, the link between graph theory and alternative algebras is studied, determining which configurations are associated with those algebras. Moreover, the isomorphism classes of each $2$-dimensional configuration associated with these algebras is analyzed, providing a new method to classify them. In order to complement the theoretical study, two algorithmic methods are implemented: the first one constructs and draws the (pseudo)digraph associated with a given alternative algebra and the second one tests if a given combinatorial structure is associated with some alternative algebra.