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 $$K_G(v) = d(v)-2$$ .

Remarks

• Baker and Norine found and proved this theorem as a discrete analogue to the classical Riemann–Roch-theorem.