A366756 Number of minimally 1-tough unlabeled graphs on n nodes.

1, 1, 1, 1, 1, 1, 2, 2, 5

Offset

1,7

Comments

A graph is minimally 1-tough if it is 1-tough but the removal of any of its edges makes it non-1-tough.

Links

Table of n, a(n) for n=1..9.

House of Graphs, Graph 536.

House of Graphs, Graph 36063.

Wikipedia, Graph toughness.

Example

For n >= 3, the cycle graph is minimally 1-tough. For 3 <= n <= 6, this is the only minimally 1-tough graph, so a(n) = 1.
For n = 7 and n = 8, the graphs with House of Graphs id's 536 and 36063, respectively, are also minimally 1-tough, and a(7) = a(8) = 2.
For n = 9, the a(9) = 5 minimally 1-tough graphs are (in graph6 format) "H?CidB?" (9-cycle), "H?Cicr_", "H?Ci[b_", "H?Ci[^o", and "H?KqKVO".

Crossrefs

Cf. A003317, A366755.

Sequence in context: A372238 A264933 A012858 * A363842 A292383 A332896

Adjacent sequences: A366753 A366754 A366755 * A366757 A366758 A366759

Keyword

nonn,more

Author

Pontus von Brömssen, Oct 20 2023

Status

approved