Riemann–Roch and Abel–Jacobi theory on a finite graph

摘要: Abstract It is well known that a finite graph can be viewed, in many respects, as discrete analogue of Riemann surface. In this paper, we pursue analogy further the context linear equivalence divisors. particular, formulate and prove graph-theoretic classical Riemann–Roch theorem. We also several results, analogous to facts about surfaces, concerning Abel–Jacobi map from its Jacobian. As an application our characterize existence or non-existence winning strategy for certain chip-firing game played on vertices graph.