A372194 Number of unlabeled graphs with n vertices and a unique triangle.

0, 0, 0, 1, 2, 7, 23, 102, 526, 3624, 32240, 382095, 5986945

Offset

0,5

Comments

The labeled version is A372172.

Links

Table of n, a(n) for n=0..12.

Gus Wiseman, The a(3) = 1 through a(6) = 23 graphs with a unique triangle.

Formula

First differences are A372174.

Example

Representatives of the a(3) = 1 through a(6) = 23 graphs:
    12,13,23    12,13,23       12,13,23             12,13,23
                14,23,24,34    12,34,35,45          12,34,35,45
                               14,23,24,34          14,23,24,34
                               12,25,34,35,45       12,25,34,35,45
                               14,25,34,35,45       12,36,45,46,56
                               15,25,34,35,45       13,23,45,46,56
                               12,14,25,34,35,45    14,25,34,35,45
                                                    15,25,34,35,45
                                                    12,14,25,34,35,45
                                                    12,23,36,45,46,56
                                                    13,23,36,45,46,56
                                                    13,25,36,45,46,56
                                                    13,26,36,45,46,56
                                                    14,25,36,45,46,56
                                                    15,26,36,45,46,56
                                                    16,26,36,45,46,56
                                                    12,13,25,36,45,46,56
                                                    12,13,26,36,45,46,56
                                                    13,23,25,36,45,46,56
                                                    14,23,25,36,45,46,56
                                                    16,23,25,36,45,46,56
                                                    13,14,23,25,36,45,46,56
                                                    13,15,23,25,36,45,46,56

Prog

(nauty) geng $n | countg -T1 # Georg Grasegger, Aug 03 2024

Crossrefs

For no triangles we have A006785, covering A372169.

Column k = 1 of A263340, covering A372173.

The labeled version is A372172.

The covering case is A372174, labeled A372171.

For all cycles (not just triangles): A236570, A372193, A372191, A372195.

A000088 counts unlabeled graphs, labeled A006125.

A001858 counts acyclic graphs, unlabeled A005195.

A002494 counts unlabeled covering graphs, labeled A006129.

A372176 counts labeled graphs by directed cycles, covering A372175.

Cf. A000055, A137917, A137918, A140637, A144958, A213434, A372168, A372170.

Sequence in context: A150387 A265797 A150388 * A073344 A038119 A006986

Adjacent sequences: A372191 A372192 A372193 * A372195 A372196 A372197

Keyword

nonn,more

Author

Gus Wiseman, Apr 24 2024

Extensions

a(11)-a(12) added by Georg Grasegger, Aug 03 2024

Status

approved