login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A124002 Triangle T(n,k) of the number of unlabeled graphs on n nodes with existential reconstruction number k, 3<=k<=n. ERN(G) is the minimum number of vertex-deleted subgraphs of G required to uniquely reconstruct G up to isomorphism. 1
4, 8, 3, 34, 0, 0, 150, 4, 2, 0, 1044, 0, 0, 0, 0, 12334, 8, 2, 2, 0, 0, 274666, 0, 2, 0, 0, 0, 0, 12005156, 6, 4, 0, 2, 0, 0, 0 (list; table; graph; refs; listen; history; text; internal format)
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 ERN and so sum(k=3,n,T(n,k))==A000088(n) for all n>=3.
LINKS
P. J. Kelly, A congruence theorem for trees, Pacific J. Math., 7 (1957), 961-968.
EXAMPLE
Triangle begins
4
8, 3
34, 0, 0
150, 4, 2, 0
1044, 0, 0, 0, 0
12334, 8, 2, 2, 0, 0
274666, 0, 2, 0, 0, 0, 0
12005156, 6, 4, 0, 2, 0, 0, 0
CROSSREFS
Sequence in context: A066199 A103647 A033197 * A014457 A365941 A365946
KEYWORD
hard,more,nice,nonn,tabl
AUTHOR
Martin Fuller, Dec 08 2006
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 28 17:25 EDT 2024. Contains 371254 sequences. (Running on oeis4.)