Study of Lie algebras by using combinatorial structures

In this paper, we study the structure and properties of those n-dimensional Lie algebras associated with either summed structures of complete graphs or some families of digraphs, having into consideration that all these combinatorial structures are made up of n vertices. Our main goal is to obtain criteria determining when a Lie algebra is associated with some of combinatorial structures considered in this paper, as well as to study the properties of those structures in order to use them as a tool for classifying the types of Lie algebras associated with them.