A326206 - OEIS

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A326206

Number of n-vertex 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 e-coefficients of incomparability graphs, arXiv:0709.0430 [math.CO], 2007.

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 A358326 A162079

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