Harmonic Labeling of Graphs

Details Harmonic Labeling of Graphs Harmonic Labeling of Graphs

2010-05-09

arxiv.org/abs/1005.1370v2

Mathematics

Combinatorics

Scientific paper

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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