Revision History for A326208
(Underlined text is an addition;
strikethrough text is a deletion.)
Showing all changes.
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#9 by Alois P. Heinz at Fri Jun 21 07:57:40 EDT 2019
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#8 by Michel Marcus at Fri Jun 21 07:04:44 EDT 2019
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#7 by Falk Hüffner at Fri Jun 21 06:29:38 EDT 2019
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#6 by Falk Hüffner at Fri Jun 21 06:29:28 EDT 2019
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| DATA
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0, 1, 0, 1, 10, 218, 10078, 896756, 151676112, 47754337568, 28229412456056, 31665593711174080
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| LINKS
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F. Hüffner, <a href="https://github.com/falk-hueffner/tinygraph">tinygraph</a>, software for generating integer sequences based on graph properties, version 9766535.
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| EXTENSIONS
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a(7)-a(11) added using tinygraph by Falk Hüffner, Jun 21 2019
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| STATUS
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approved
editing
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#5 by Susanna Cuyler at Sun Jun 16 22:33:13 EDT 2019
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#4 by Gus Wiseman at Sun Jun 16 12:20:36 EDT 2019
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#3 by Gus Wiseman at Sun Jun 16 12:18:45 EDT 2019
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| CROSSREFS
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The casedirected withoutversion ais HamiltonianA326204 (with cycleloops) or isA326219 (without A326207.loops).
TheSimple graphs casenot withcontaining a Hamiltonian pathcycle isare A326206A326207.
TheSimple graphs containing casea forHamiltonian digraphspath isare A326204A326206.
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#2 by Gus Wiseman at Sat Jun 15 05:31:36 EDT 2019
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| NAME
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allocatedNumber of Hamiltonian labeled simple graphs forwith Gusn Wisemanvertices.
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| DATA
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0, 1, 0, 1, 10, 218, 10078
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| OFFSET
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0,5
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| COMMENTS
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A graph is Hamiltonian if it contains a cycle passing through every vertex exactly once.
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| LINKS
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Wikipedia, <a href="https://en.wikipedia.org/wiki/Hamiltonian_path">Hamiltonian path</a>
Gus Wiseman, <a href="/A326208/a326208.png">The a(5) = 218 simple graphs containing a Hamiltonian cycle.</a>
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| FORMULA
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A006125(n) = a(n) + A326207(n).
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| MATHEMATICA
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Table[Length[Select[Subsets[Subsets[Range[n], {2}]], FindHamiltonianCycle[Graph[Range[n], #]]!={}&]], {n, 0, 4}] (* Mathematica 8.0+ *)
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| CROSSREFS
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The unlabeled version is A003216.
The case without a Hamiltonian cycle is A326207.
The case with a Hamiltonian path is A326206.
The case for digraphs is A326204.
Cf. A003216, A006125, A057864, A283420.
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| KEYWORD
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allocated
nonn,more
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| AUTHOR
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Gus Wiseman, Jun 15 2019
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approved
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#1 by Gus Wiseman at Thu Jun 13 20:11:10 EDT 2019
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| NAME
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allocated for Gus Wiseman
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| KEYWORD
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allocated
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approved
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