Let a graph 
be defined on vertex set 
and edge set 
. Then a construction sequence (or c-sequence) for 
is a linear order on 
in which each edge appears after both of its endpoints.
The construction number 
of 
is then defined as the number of distinct construction sequences
for 
(Kainen 2023).
For example, for the path graph 
with vertex set 1, 2, 3 and
edge set 12, 23, there are 16 possible construction sequences
(so 
),
one of which is (1, 2, 3, 23, 13) (Kainen 2023).
The construction numbers for a number of parametrized graph are summarized in the table below (cf. Kainen 2023), where 
is a Bernoulli number.
| family | OEIS | construction number |
complete
graph  | A098694 |  |
cycle graph  | A024255 |  |
empty graph  | A000142 |  |
ladder rung graph  | A210277 |  |
path graph  | A000182 |  |
star graph  | A055546 |  |
