A graph 
is said to be hypomorphic to a graph 
if 
and 
have the same graph deck. Equivalently,
is hypomorphic to 
precisely when the vertices of 
and 
can be put in bijection, say
by 
,
so that the graph card 
is isomorphic to 
for every vertex 
of 
.
A graph is reconstructible if it has no nonisomorphic hypomorphic mate. The graph reconstruction conjecture asserts that every simple finite graph on at least three vertices is reconstructible.
