Jacobian tori associated with a finite graph and its abelian covering graphs

Abstract

We develop a graph-theoretic analogue of the Jacobian torus, which is defined, for a finite graph X, as the torus H1(X,R)/H1(X,Z) with a natural flat metric. It is observed that this notion, especially the volume of Jacobian tori, appears in many contexts of graph theory. © 2000 Academic Press.