

A124003


Triangle T(n,k) of the number of unlabeled graphs on n nodes with universal reconstruction number k, 3<=k<=n. URN(G) is the minimum size for which all multisubsets of vertexdeleted subgraphs of G can uniquely reconstruct G up to isomorphism.


1



3, 2, 9, 7, 19, 8, 8, 56, 90, 2, 16, 496, 520, 12, 0, 266, 8308, 3584, 284, 4, 0, 45186, 199247, 28781, 1434, 20, 0, 0, 6054148, 5637886, 301530, 10686, 914, 4, 0, 0
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OFFSET

3,1


COMMENTS

The (vertex) Reconstruction Conjecture, due to Kelly and Ulam, states that every graph with three or more vertices is reconstructible up to isomorphism given the multiset of vertex deleted subgraphs. Equivalently, every graph has an URN and so sum(k=3,n,T(n,k))==A000088(n) for all n>=3.


LINKS

Table of n, a(n) for n=3..38.
P. J. Kelly, A congruence theorem for trees, Pacific J. Math., 7 (1957), 961968.
B. McMullen, Graph reconstruction numbers.
Wikipedia, Reconstruction conjecture.


EXAMPLE

Triangle begins
3
2 9
7 19 8
8 56 90 2
16 496 520 12 0
266 8308 3584 284 4 0
45186 199247 28781 1434 20 0 0
6054148 5637886 301530 10686 914 4 0 0


CROSSREFS

Cf. A124002, A000088, A006652A006655.
Sequence in context: A084398 A118306 A237651 * A159588 A321572 A118045
Adjacent sequences: A124000 A124001 A124002 * A124004 A124005 A124006


KEYWORD

hard,more,nice,nonn,tabl


AUTHOR

Martin Fuller, Dec 08 2006


STATUS

approved



