Isolated Point


An isolated point of a graph is a node of degree 0 (Hartsfield and Ringel 1990, p. 8; Harary 1994, p. 15; D'Angelo and West 2000, p. 212;
West 2000, p. 22). The number of -node graphs with
no isolated points are 0, 1, 2, 7, 23, 122, 888, ... (Sloane's A002494),
the first few of which are illustrated above. The number of graphical
partitions of length
is equal to the number of
-node graphs that
have no isolated points.
Connected graphs have no isolated points.
An isolated point on a curve is more commonly known as an acnode.
An isolated point of a discrete set is a member of
(Krantz 1999, p. 63).