Critical groups of covering, voltage and signed graphs

Victor Reiner, Dennis Tseng

Research output: Contribution to journalArticle

2 Scopus citations

Abstract

Graph coverings are known to induce surjections of their critical groups. Here we describe the kernels of these morphisms in terms of data parametrizing the covering. Regular coverings are parametrized by voltage graphs, and the above kernel can be identified with a naturally defined voltage graph critical group. For double covers, the voltage graph is a signed graph, and the theory takes a particularly pleasant form, leading also to a theory of double covers of signed graphs.

Original languageEnglish (US)
Pages (from-to)10-40
Number of pages31
JournalDiscrete Mathematics
Volume318
Issue number1
DOIs
StatePublished - Mar 6 2014

Keywords

  • Covering
  • Critical
  • Crown
  • Double
  • Functorial
  • Graph
  • Morphism
  • Sandpile group
  • Signed
  • Voltage

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