A spider graph, spider tree, or simply "spider," is a tree with one vertex of vertex
degree at least 3 and all others with vertex degree
at most 2. The numbers of spiders on , 2, ... nodes are 0, 0,
0, 1, 2, 4, 7, 11, 17, 25, 36, 50, 70, 94, ... (OEIS A004250).
The count
of spider trees with nodes is the same as the number of integer
partitions of
into three or more parts. It also has closed form
Gallian, J. "Dynamic Survey of Graph Labeling." Elec. J. Combin., Dynamic Survey DS6, Oct. 30, 2025. https://doi.org/10.37236/27.Levit,
V. E. and Mandrescu, E. "The Independence Polynomial of a Graph--A Survey."
In Proceedings of the 1st International Conference on Algebraic Informatics. Held
in Thessaloniki, October 20-23, 2005 (Ed. S. Bozapalidis, A. Kalampakas,
and G. Rahonis). Thessaloniki, Greece: Aristotle Univ., pp. 233-254, 2005.Sloane,
N. J. A. Sequence A004250/M1046
in "The On-Line Encyclopedia of Integer Sequences."
, 2, ... nodes are 0, 0,
0, 1, 2, 4, 7, 11, 17, 25, 36, 50, 70, 94, ... (OEIS A004250).
of spider trees with 
nodes is the same as the number of integer
partitions of 
into three or more parts. It also has closed form
is the partition function P and 
is the floor
function. A generating function for 
is given by
is a q-Pochhammer symbol.
