

A033483


Number of disconnected 4valent (or quartic) graphs with n nodes.


18



0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 3, 8, 25, 88, 378, 2026, 13351, 104595, 930586, 9124662, 96699987, 1095469608, 13175272208, 167460699184, 2241578965849
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OFFSET

0,13


COMMENTS

Despite A006820(n) being currently unknown for n > 21, we can calculate this sequence A033483(n) up to n = 26, because the smallest 4regular graph is K_5.  Jason Kimberley, Sep 27 2009


REFERENCES

R. C. Read and R. J. Wilson, An Atlas of Graphs, Oxford, 1998.


LINKS

Table of n, a(n) for n=0..26.
Jason Kimberley, Index of sequences counting disconnected kregular simple graphs with girth at least g
N. J. A. Sloane, Transforms
Eric Weisstein's World of Mathematics, Disconnected Graph
Eric Weisstein's World of Mathematics, Quartic Graph


FORMULA

A033483 = A033301  A006820 = Euler_transformation(A006820)  A006820.
a(n) = A068933(n, 4).  Jason Kimberley, Sep 27 2009 and Jan 08 2011


CROSSREFS

4regular simple graphs: A006820 (connected), this sequence (disconnected), A033301 (not necessarily connected).  Jason Kimberley, Jan 08 2011
Disconnected regular simple graphs: A068932 (any degree), A068933 (triangular array), specified degree k: A165652 (k=2), A165653 (k=3), this sequence (k=4), A165655 (k=5), A165656 (k=6), A165877 (k=7), A165878 (k=8), A185293 (k=9), A185203 (k=10), A185213 (k=11).
Disconnected 4regular simple graphs with girth at least g: this sequence (g=3), A185244 (g=4), A185245 (g=5), A185246 (g=6).
Sequence in context: A244278 A190343 A185043 * A130522 A006219 A009268
Adjacent sequences: A033480 A033481 A033482 * A033484 A033485 A033486


KEYWORD

nonn,nice,hard,more


AUTHOR

R. C. Read (rcread(AT)math.uwaterloo.ca)


EXTENSIONS

3 more terms from Martin Fuller, Dec 04 2006
Terms a(19)a(24) from Jason Kimberley, Sep 27 2009
Comment updated, and new terms a(25) and a(26) appended by Jason Kimberley, Dec 30 2010


STATUS

approved



