# Riemann-Roch-theorem of Baker and Norine

$\rm{rank}(D) − \rm{rank}(K_G − D) = \deg(D) + 1 − g$,

where

• $D$ is any divisor on graph $G$,
• $g = |E(G)|-|V(G)| + 1$ (the genus of the graph,) and
• $K$ is the canoncial divisor of $G$, defined as $K_G(v) = d(v)-2$.

## References

1. M. Baker, S. Norine, Riemann--Roch and Abel--Jacobi theory on a finite graph, Advances in Mathematics (2007) DOI link, ArXiv Link