I believe one of the first paper was:
Bacher, Roland; de la Harpe, Pierre; Nagnibeda, Tatiana The lattice of integral flows and the lattice of integral cuts on a finite graph. (English) Zbl 0891.05062The lattice of integral flows and the lattice of integral cuts on a finite graph, Bull. Soc. Math. Fr. 125125, No. 2, 167-198 (1997). Zbl 0891.05062
(Sorry, self-promotion).
It has been widely cited by subsequent papers on the subject (use MathSciNet or Zentralblatt)
I remember also a one or two interesting papers by Mathew Baker (you can find them by looking through the papers citing the above paper) on the subject.