Harmonic Labeling of Graphs
classification
🧮 math.CO
math.GR
keywords
harmoniclabelingfunctiongraphgraphsadmitcallconstructed
read the original 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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