Elsevier

Applied Mathematics Letters

Volume 16, Issue 8, November 2003, Pages 1329-1332
Applied Mathematics Letters

Semiharmonic trees and monocyclic graphs

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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.

Keywords

Walks in graphs
Harmonic graphs
Trees
Monocyclic graph
Cyclomatic number

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The authors would like to thank the DFG for support.