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.