An important quantity associated to a graph divisor is its rank. We denote <math>Div(G)</math> denotes the set of all graph divisors by on a graph <math>Div(G)</math>. We call a A graph divisor <math>D</math> is ''effective'' if <math>D(v) \ge 0 </math> for all <math>v \in V</math>. We call a A graph divisor <math>D</math> is ''equi-effective'' if there exist <math>0 \le D' \in Div(G)(v) </math> such that <math>D \sim D'</math>.
'''Definition'''(The rank of divisor <math>D</math>)
=== Remarks ===
* V. Kiss and L. Tóthmérész proved that determining Determining the rank of a graph divisor is '''NP'''-hard, even in on simple undirected graphs <ref name="KT15"/>.
* The most well-known theorem about this rank function is the [[Riemann--Roch-theorem of Baker and Norine]] <ref name="BN07"/>.
