A spider graph, spider tree, or simply "spider," is a tree with one vertex of degree at least 3 and all others with 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
 |
(1)
|
where 
is the partition function P and 
is the floor function.
A generating function for 
is given by
 |  |  |
(2)
|
 |  |  |
(3)
|
 |  |  |
(4)
|
where 
is a q-Pochhammer symbol.
Not all spiders are caterpillar graphs, nor are all spiders lobster graphs.
