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Isolated Point

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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 n-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 n is equal to the number of n-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 S is a member of S (Krantz 1999, p. 63).

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