Semiharmonic trees and monocyclic graphs |
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| Authors: | A. Dress,S. Grü newald, |
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| Affiliation: | Forschungsschwerpunkt Mathematisierung, Universität Bielefeld Postfach 100131, 33501, Bielefeld, Germany |
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| Abstract: | A graph G is defined to be semiharmonic if there is a constant μ (necessarily a natural number) such that, for every vertex v, the number of walks of length 3 starting in v equals μdG(v) where dG(v) is the degree of v. We determine all finite semiharmonic trees and monocyclic graphs. |
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| Keywords: | Walks in graphs Harmonic graphs Trees Monocyclic graph Cyclomatic number |
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