Harmonic Labeling of Graphs
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$.
 Publication:

arXiv eprints
 Pub Date:
 May 2010
 arXiv:
 arXiv:1005.1370
 Bibcode:
 2010arXiv1005.1370B
 Keywords:

 Mathematics  Combinatorics;
 Mathematics  Group Theory