An isolated vertex of a graph is a graph vertex of vertex degree 0. Terminology is not
uniform: Hartsfield and Ringel (1990, p. 8), D'Angelo and West (2000, p. 212),
and West (2000, p. 22) use isolated vertex, while Harary (1994, p. 15)
uses isolated point.
The numbers of -vertex
graphs with no isolated vertices are 0, 1, 2, 7, 23, 122, 888, ... (OEIS A002494),
the first few of which are illustrated above. The number of graphical
partitions of length is equal to the number of -vertex graphs that have no isolated vertices.
A connected graph with more than one vertex has
no isolated vertices.
-vertex
graphs with no isolated vertices are 0, 1, 2, 7, 23, 122, 888, ... (OEIS A002494),
the first few of which are illustrated above. The number of graphical
partitions of length 
is equal to the number of 
-vertex graphs that have no isolated vertices.
