Graph theory and finite-dimensional flexible algebras

Abstract

In this paper, the link between graph theory and flexible algebras is studied, determining which configurations are associated with those algebras. We also deal with the properties of flexible algebras that can be read from their associated graph. 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 flexible algebra and the second one tests if a given combinatorial structure is associated with some flexible algebra.