(Pseudo)digraphs and Leibniz algebra isomorphisms: (Pseudo)digraphs and Leibniz algebra isomorphisms

This paper studies the link between isomorphic digraphs and isomorphic Leibniz algebras, determining in detail this fact when using (psuedo) digraphs of 2 and 3 vertices associated with Leibniz algebras according to their isomorphism classes. Moreover, we give the complete list with all the combinatorial structures of 3 vertices associated with Leibniz algebras, studying their isomorphism classes. We also compare our results with the current classifications of 2- and 3-dimensional Leibniz algebras. Finally, we introduce and implement the algorithmic procedure used for our goals and devoted to decide if a given combinatorial structure is associated or not with a Leibniz algebra.