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

Author

Gus Wiseman, Apr 24 2024

Keywords

• nonn
• more

Comments

The labeled version is A372172.

Examples

			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
		

Links

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

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.

Programs

nauty

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

Formula

First differences are A372174.

Extensions

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