The subgraph isomorphism problem asks, for two finite graphs 
and 
, whether 
contains a subgraph isomorphic
to 
. The problem is NP-complete;
the clique decision problem
is obtained by taking 
to be a complete graph.
Unlike graph isomorphism, the subgraph problem allows graph vertices and graph
edges of 
to be discarded. The induced subgraph isomorphism problem
additionally requires the copy of 
to be a vertex-induced
subgraph.
