

A326206


Number of nvertex labeled simple graphs containing a Hamiltonian path.


10



0, 0, 1, 4, 34, 633, 23368, 1699012, 237934760, 64558137140, 34126032806936, 35513501049012952
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

0,4


COMMENTS

A path is Hamiltonian if it passes through every vertex exactly once.


LINKS

Table of n, a(n) for n=0..11.
F. Hüffner, tinygraph, software for generating integer sequences based on graph properties, version 9766535.
Wikipedia, Hamiltonian path
Gus Wiseman, Enumeration of paths and cycles and ecoefficients of incomparability graphs.
Gus Wiseman, The a(4) = 34 simple graphs containing a Hamiltonian path


FORMULA

A006125(n) = a(n) + A326205(n).


MATHEMATICA

Table[Length[Select[Subsets[Subsets[Range[n], {2}]], FindHamiltonianPath[Graph[Range[n], #]]!={}&]], {n, 0, 4}] (* Mathematica 10.2+ *)


CROSSREFS

The unlabeled case is A057864.
The directed case is A326214 (with loops) or A326217 (without loops).
Simple graphs without a Hamiltonian path are A326205.
Simple graphs with a Hamiltonian cycle are A326208.
Cf. A003216, A006125, A057864, A283420.
Sequence in context: A333981 A030243 A222789 * A088077 A162079 A353041
Adjacent sequences: A326203 A326204 A326205 * A326207 A326208 A326209


KEYWORD

nonn,more


AUTHOR

Gus Wiseman, Jun 14 2019


EXTENSIONS

a(7)a(11) added using tinygraph by Falk Hüffner, Jun 21 2019


STATUS

approved



