A283420
Number of simple (not necessarily connected) untraceable graphs on n nodes.
Original entry on oeis.org
0, 1, 2, 6, 16, 65, 310, 2316, 26241, 522596, 18766354
Offset: 1
Cf.
A000088 (number of simple graphs on n vertices).
Cf.
A057864 (number of simple traceable graphs on n vertices).
Cf.
A283421 (number of simple connected untraceable graphs on n vertices).
The directed case is
A326224 (with loops).
Unlabeled simple graphs not containing a Hamiltonian cycle are
A246446.
A326221
Number of unlabeled n-vertex digraphs (with loops) containing a Hamiltonian path.
Original entry on oeis.org
0, 0, 7, 74, 2395
Offset: 0
The undirected case is
A057864 (without loops).
Unlabeled digraphs not containing a Hamiltonian path are
A326224.
Unlabeled digraphs containing a Hamiltonian cycle are
A326226.
A326220
Number of non-Hamiltonian labeled n-vertex digraphs (with loops).
Original entry on oeis.org
1, 0, 12, 392, 46432, 20023232, 30595305216
Offset: 0
The a(2) = 12 digraph edge-sets:
{} {11} {11,12} {11,12,22}
{12} {11,21} {11,21,22}
{21} {11,22}
{22} {12,22}
{21,22}
The undirected case is
A326239 (with loops) or
A326207 (without loops).
Digraphs (with loops) containing a Hamiltonian cycle are
A326204.
Digraphs (with loops) not containing a Hamiltonian path are
A326213.
-
Table[Length[Select[Subsets[Tuples[Range[n],2]],FindHamiltonianCycle[Graph[Range[n],DirectedEdge@@@#]]=={}&]],{n,4}] (* Mathematica 8.0+. Warning: Using HamiltonianGraphQ instead of FindHamiltonianCycle returns a(4) = 46336 which is incorrect *)
A326223
Number of non-Hamiltonian unlabeled n-vertex digraphs (with loops).
Original entry on oeis.org
1, 0, 7, 80, 2186
Offset: 0
Non-isomorphic representatives of the a(2) = 7 digraph edge-sets:
{}
{11}
{12}
{11,12}
{11,21}
{11,22}
{11,12,22}
The undirected case is
A246446 (without loops) or
A326239 (with loops).
Hamiltonian unlabeled digraphs are
A326226.
Unlabeled digraphs not containing a Hamiltonian path are
A326224.
A326213
Number of labeled n-vertex digraphs (with loops) not containing a (directed) Hamiltonian path.
Original entry on oeis.org
1, 2, 4, 128, 12352, 3826272, 3775441536
Offset: 0
Digraphs containing a Hamiltonian path are
A326214.
Digraphs not containing a Hamiltonian cycle are
A326220.
-
Table[Length[Select[Subsets[Tuples[Range[n],2]],FindHamiltonianPath[Graph[Range[n],DirectedEdge@@@#]]=={}&]],{n,0,3}] (* Mathematica 10.2+ *)
A326214
Number of labeled n-vertex digraphs (with loops) containing a (directed) Hamiltonian path.
Original entry on oeis.org
0, 0, 12, 384, 53184
Offset: 0
The a(2) = 12 edge-sets:
{12}
{21}
{11,12}
{11,21}
{12,21}
{12,22}
{21,22}
{11,12,21}
{11,12,22}
{11,21,22}
{12,21,22}
{11,12,21,22}
Digraphs not containing a Hamiltonian path are
A326213.
Digraphs containing a Hamiltonian cycle are
A326204.
-
Table[Length[Select[Subsets[Tuples[Range[n],2]],FindHamiltonianPath[Graph[Range[n],DirectedEdge@@@#]]!={}&]],{n,4}] (* Mathematica 10.2+ *)
A326216
Number of labeled n-vertex digraphs (without loops) not containing a (directed) Hamiltonian path.
Original entry on oeis.org
1, 1, 1, 16, 772
Offset: 0
The a(3) = 16 edge-sets:
{} {12} {12,13}
{13} {12,21}
{21} {12,32}
{23} {13,23}
{31} {13,31}
{32} {21,23}
{21,31}
{23,32}
{31,32}
Unlabeled digraphs not containing a Hamiltonian path are
A326224.
The unlabeled undirected case is
A283420.
Digraphs (without loops) containing a Hamiltonian path are
A326217.
Digraphs (without loops) not containing a Hamiltonian cycle are
A326218.
-
Table[Length[Select[Subsets[Select[Tuples[Range[n],2],UnsameQ@@#&]],FindHamiltonianPath[Graph[Range[n],DirectedEdge@@@#]]=={}&]],{n,4}] (* Mathematica 10.2+ *)
A326222
Number of non-Hamiltonian unlabeled n-vertex digraphs (without loops).
Original entry on oeis.org
1, 0, 2, 12, 157, 5883, 696803, 255954536
Offset: 0
The undirected case (without loops) is
A246446.
Hamiltonian unlabeled digraphs are
A326225 (without loops) or
A003216 (with loops).
Showing 1-8 of 8 results.
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