A Riemann-Roch Theorem on Infinite Graphs

Atsushi Atsuji, Hiroshi Kaneko

Research output: Chapter in Book/Report/Conference proceedingChapter


A Riemann-Roch theorem on graph was initiated by M.Baker and S.Norine. In their article, a Riemann-Roch theorem on a finite graph with uniform unit vertex-weight and uniform unit edge-weight was established and a feasibility of Riemann-Roch theorem on infinite graph was suggested. In this article, we take an edge-weighted infinite graph and focus on the importance of the spectral gaps of the Laplace operators defined on its finite subgraphs naturally given by ℚ -valued positive weights on the edges. We build a potential theoretic scheme for a proof of a Riemann-Roch theorem on the edge-weighted infinite graphs.

Original languageEnglish
Title of host publicationSTEAM-H
Subtitle of host publicationScience, Technology, Engineering, Agriculture, Mathematics and Health
PublisherSpringer Nature
Number of pages16
Publication statusPublished - 2021

Publication series

NameSTEAM-H: Science, Technology, Engineering, Agriculture, Mathematics and Health
ISSN (Print)2520-193X
ISSN (Electronic)2520-1948


  • Infinite graphs
  • Laplace operator on graphs
  • Riemann-Roch theorem

ASJC Scopus subject areas

  • General Computer Science
  • General Chemistry
  • Modelling and Simulation
  • General Agricultural and Biological Sciences
  • General Engineering
  • Economics, Econometrics and Finance(all)
  • Applied Mathematics


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