A new characterization of equipartite graphs

A graph G of order 2n is called equipartite if for every n-element set A⊆V(G), there exists an automorphism of G that maps the induced subgraph G[A] onto G[V(G)∖A]. In this paper, we show that a graph G of order 2n is equipartite if and only if for every such partition of V(G), the induced subgraphs G[A] and G[V(G)∖A] have the same Laplacian spectra.