Two-Regular Graph

A two-regular graph is a regular graph for which all local degrees are 2. A two-regular graph consists of one or more (disconnected) cycles.


The numbers a_n of two-regular graphs on n=1, 2, ... nodes are 0, 0, 1, 1, 1, 2, 2, 3, 4, 5, ... (OEIS A008483), which are equivalent to the numbers of partitions of n into parts >=3. The first few such graphs are illustrated above.

This sequence has closed form


where P(n) is the partition function P. It also has generating function given by


where (x)_infty is a q-Pochhammer symbol.

See also

Cycle Graph, Empty Graph, Regular Graph

Explore with Wolfram|Alpha


Sloane, N. J. A. Sequence A008483 in "The On-Line Encyclopedia of Integer Sequences."

Cite this as:

Weisstein, Eric W. "Two-Regular Graph." From MathWorld--A Wolfram Web Resource.

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