A Riemann-Roch theorem for edge-weighted graphs
Rodney James, Rick Miranda
TL;DR
This paper extends the Riemann-Roch theorem to real divisors on edge-weighted graphs, broadening the mathematical framework from integral divisors to real weights, and generalizing previous results.
Contribution
It introduces a Riemann-Roch theorem for real divisors on edge-weighted graphs, expanding the scope of algebraic graph theory beyond integral divisors.
Findings
Proves a Riemann-Roch theorem for real divisors on edge-weighted graphs
Generalizes Baker and Norine's theorem from integral to real divisors
Extends the theory to graphs with multiple edges
Abstract
We prove a Riemann-Roch theorem for real divisors on edge-weighted graphs over the reals, extending the result of Baker and Norine for integral divisors on graphs with multiple edges.
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