Superregular Graph
For a Vertex 
of a Graph, let 
and 
denote the Subgraphs of 
induced by the Vertices adjacent to andnonadjacent to , respectively. The empty graph is defined to be superregular, and 
is said to be superregularif is a Regular Graph and both and are superregular for all .
The superregular graphs are precisely 
, 
(
), 
(
), and the complements of these graphs,where 
is a Cyclic Graph, 
is a Complete Graph and is 
disjoint copies of , and is the Cartesian product of with itself (the graph whose Vertex set consists of 
Vertices arranged in an 
square with two Vertices adjacentIff they are in the same row or column).
References
Vince, A. ``The Superregular Graph.'' Problem 6617. Amer. Math. Monthly 103, 600-603, 1996. West, D. B. ``The Superregular Graphs.'' J. Graph Th. 23, 289-295, 1996.
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