Abstract
An analysis of the Riemann Roch theorem for finite graphs was formulated and proved by Baker and Norine in 2006. In this work, we introduce a partial order on the divisor group of a finite graph and prove some results, which are useful in giving a simple proof of the Riemann Roch Theorem on finite graphs. We also establish a one-to-one correspondence between the exceptional set and a certain subset of acyclic orientations for a graph.
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