Vince and Bóna (2012) define an assembly tree 
for a connected simple graph 
on 
nodes as a binary rooted
tree with 
leavesTree Leaf and 
internal nodes and satisfying a number of additional properties. An assembly tree
for 
describes a process motivated by considering the self-assembly
of macromolecules performed by virus capsids in the host cell (Kainen 2023).
The assembly number 
of a graph 
gives the number of assembly trees from which 
can be built. These numbers therefore count ways to build
up a graph from subgraphs induced by various subsets of the vertices (Kainen 2023).
The assembly numbers for a number of parametrized graph are summarized in the table below (cf. Vince and Bóna 2012), where 
is a Catalan number and
is a double
factorial.
