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In this talk we propose a graphical representation of some classes of Leibniz algebras. With each of algebra from these classes we associate a graph. This assignment enables us to reformulate some structural properties of the Leibniz algebras in terms of some conditions for the graphs. The talk focuses on a so-called filiform Leibniz algebras. It is well-known that this class is split into three subclasses called first, second and third class denoted, in dimension n over a field K, by FLbn(K), SLbn(K) and TLbn(K), respectively. In this article, we concern more on the combinatorial structures associated with SLbn(K) in low-dimensions.

Combinatorial structures associated with low dimensional second class of non-Lie filiform Leibniz algebra