The graph deck, or vertex deck, of a graph 
is the multiset of one-vertex-deleted
vertex-induced subgraphs 
as 
ranges over the vertices of 
,
usually considered up to graph isomorphism and
with multiplicity. The terminology is by analogy with a deck of playing cards: the
graph deck is the multiset of graph
cards, and repeated isomorphic cards are retained with multiplicity. The illustration
above shows a graph together with its graph deck, displayed as the collection of
all one-vertex-deleted cards. Two graphs with the same deck are said to be hypomorphic.
The graph reconstruction conjecture asserts that every simple finite graph on at least three vertices is determined up to isomorphism by its graph deck.
