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arXiv · 1005.1370

Harmonic Labeling of Graphs

Itai Benjamini·Van Cyr·Eviatar B. Procaccia·Ran J. Tessler
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Abstract

Which graphs admit an integer value harmonic function which is injective and surjective onto $\Z$? Such a function, which we call harmonic labeling, is constructed when the graph is the $\Z^2$ square grid. It is shown that for any finite graph $G$ containing at least one edge, there is no harmonic labeling of $ G \times \Z$.

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Itai Benjamini, Van Cyr, Eviatar B. Procaccia, Ran J. Tessler. 2010-05-30. Harmonic Labeling of Graphs. https://arxiv.org/abs/1005.1370

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