Equipartite graphs.

A graph G of even order is weakly equipartite if for any partition of its vertex set into subsets V ₁ and V ₂ of equal size the induced subgraphs G[ V ₁] and G[ V ₂] are isomorphic. A complete characterization of (weakly) equipartite graphs is derived. In particular, we show that each such graph is vertex-transitive. In a subsequent paper, we use these results to characterize equipartite polytopes, a geometric analogue of equipartite graphs. [ABSTRACT FROM AUTHOR]