For a graph vertex 
of a graph, let 
and 
denote the subgraphs of
induced by the graph vertices adjacent to and nonadjacent
to 
,
respectively. The empty graph is defined to be superregular, and 
is said to be superregular if 
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 graph
vertex set consists of 
graph vertices arranged
in an 
square with two graph vertices adjacent iff
they are in the same row or column).
