For a graph vertex x of a graph, let Γ_x and Δ_x denote the subgraphs of Γ - x induced by the graph vertices adjacent to and nonadjacent to x, respectively. The empty graph is defined to be superregular, and Γ is said to be superregular if Γ is a regular graph and both Γ_x and Δ_x are superregular for all x.

complete graph | cyclic graph | regular graph