Harmonic trees |
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Authors: | S Grünewald |
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Institution: | Forschungsschwerpunkt Mathematisierung Universität Bielefeld Postfach 100131 33501, Bielefeld, Germany |
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Abstract: | 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
, and we give a recursive construction for all infinite harmonic trees. |
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Keywords: | Harmonic graphs Walks in graphs Finite and infinite trees |
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