2010/05/09 by Itaï Benjamini, Itai Benjamini, Van Cyr +6
Computer Science · Engineering · Mathematics · #Acoustics #Combinatorics #Combinatorics (math.CO) #Digital Image Processing Techniques #Discrete mathematics #FOS: Mathematics #Graph #Graph Labeling and Dimension Problems #Group Theory (math.GR) #Harmonic #Harmonic function #Injective function #Mathematical analysis #Mathematics #Physics #Surjective function #graph theory and CDMA systems #math.CO #math.GR
paper · pdf · doi:10.48550/arxiv.1005.1370
published in arXiv (Cornell University) (Cornell University)
openalex publication_date 2010/05/09 · arxiv created 2010/05/30 · arxiv updated 2010/06/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 \Z2 square grid. It is shown that for any finite graph G containing at least one edge, there is no harmonic labeling of G × \Z.