Harmonic trees Original Research Article

A graph G is defined to be harmonic if there is a constant λ (necessarily a natural number) such that, for every vertex v, the sum of the degrees of the neighbors of v equals λdG (v) where dG (v) is the degree of v. We show that there is exactly one finite harmonic tree for every λ ϵ View the MathML source, and we give a recursive construction for all infinite harmonic trees.