Automorphism groups of nilpotent Lie algebras associated to certain graphs
Abstract We consider a family of 2-step nilpotent Lie algebras associated to uniform complete graphs on odd number of vertices. We prove that the symmetry group of such a graph is the holomorph of the additive cyclic group Moreover, we prove that the (Lie) automorphism group of the corresponding nilpotent Lie algebra contains the dihedral group of order as a subgroup.