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URL: https://oeis.org/A001434

⇱ A001434 - OEIS

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A001434
Number of graphs with n nodes and n edges.
16
1, 0, 0, 1, 2, 6, 21, 65, 221, 771, 2769, 10250, 39243, 154658, 628635, 2632420, 11353457, 50411413, 230341716, 1082481189, 5228952960, 25945377057, 132140242356, 690238318754, 3694876952577, 20252697246580, 113578669178222, 651178533855913, 3813856010041981
OFFSET
0,5
COMMENTS
The labeled version is A116508. - Gus Wiseman, Feb 22 2024
REFERENCES
J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 146.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..50 (terms 1..40 from Sean A. Irvine)
CombOS - Combinatorial Object Server, Generate graphs
M. L. Stein and P. R. Stein, Enumeration of Linear Graphs and Connected Linear Graphs up to p = 18 Points. Report LA-3775, Los Alamos Scientific Laboratory of the University of California, Los Alamos, NM, Oct 1967.
EXAMPLE
From Gus Wiseman, Feb 22 2024: (Start)
Representatives of the a(0) = 1 through a(5) = 6 graphs:
{} . . {12,13,23} {12,13,14,23} {12,13,14,15,23}
{12,13,24,34} {12,13,14,23,24}
{12,13,14,23,25}
{12,13,14,23,45}
{12,13,14,25,35}
{12,13,24,35,45}
(End)
MATHEMATICA
(* first do *) Needs["Combinatorica`"] (* then *) Table[ NumberOfGraphs[n, n], {n, 24}] (* Robert G. Wilson v, Mar 22 2011 *)
brute[m_]:=First[Sort[Table[Sort[Sort /@ (m/.Rule@@@Table[{(Union@@m)[[i]], p[[i]]}, {i, Length[p]}])], {p, Permutations[Range[Length[Union@@m]]]}]]];
Table[Length[Union[brute /@ Subsets[Subsets[Range[n], {2}], {n}]]], {n, 0, 5}] (* Gus Wiseman, Feb 22 2024 *)
PROG
(PARI) a(n) = polcoef(G(n, O(x*x^n)), n) \\ G defined in A008406. - Andrew Howroyd, Feb 02 2024
CROSSREFS
The connected case is A001429, labeled A057500.
The covering case is A006649, labeled A367863.
Diagonal n = k of A008406.
The labeled version is A116508.
The version with loops is A368598, connected A368983.
Allowing up to n edges gives A370315, labeled A369192.
A000088 counts unlabeled graphs, labeled A006125.
A001349 counts unlabeled connected graphs, labeled A001187.
A002494 counts unlabeled covering graphs, labeled A006129.
Sequence in context: A228394 A245749 A342440 * A119098 A294706 A294707
KEYWORD
nonn,easy,nice
EXTENSIONS
More terms from Vladeta Jovovic, Jan 07 2000
a(0)=1 prepended by Andrew Howroyd, Feb 02 2024
STATUS
approved