Vince and Bóna (2012) define an assembly tree 
for a connected simple graph 
on 
nodes as a binary rooted
tree with 
leaves 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 double factorial.
| family | OEIS | assembly number |
complete
bipartite graph  | A217523 | |
complete graph  | A001147 |  |
complete tripartite
graph  | A361072 | |
cycle graph  | A001700 |  |
path graph  | A000108 |  |
star graph  | A000142 |  |
If 
is a Hamiltonian graph on 
vertices, then
 |
where 
denotes the cycle graph on 
vertices. Similarly, if 
is a nonhamiltonian graph
on 
vertices with a Hamiltonian path, then
 |
where 
denotes the path graph on 
vertices.
