OFFSET
0,5
COMMENTS
These are simple graphs covering n vertices such that some connected component has at least two cycles.
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..50
EXAMPLE
Representatives of the a(4) = 2 and a(5) = 13 simple graphs:
{12}{13}{14}{23}{24} {12}{13}{14}{15}{23}{24}
{12}{13}{14}{23}{24}{34} {12}{13}{14}{15}{23}{45}
{12}{13}{14}{23}{24}{35}
{12}{13}{14}{23}{25}{45}
{12}{13}{14}{25}{35}{45}
{12}{13}{14}{15}{23}{24}{25}
{12}{13}{14}{15}{23}{24}{34}
{12}{13}{14}{15}{23}{24}{35}
{12}{13}{14}{23}{24}{35}{45}
{12}{13}{14}{15}{23}{24}{25}{34}
{12}{13}{14}{15}{23}{24}{35}{45}
{12}{13}{14}{15}{23}{24}{25}{34}{35}
{12}{13}{14}{15}{23}{24}{25}{34}{35}{45}
MATHEMATICA
brute[m_]:=First[Sort[Table[Sort[Sort /@ (m/.Rule@@@Table[{(Union@@m)[[i]], p[[i]]}, {i, Length[p]}])], {p, Permutations[Range[Length[Union@@m]]]}]]];
Table[Length[Union[brute /@ Select[Subsets[Subsets[Range[n], {2}]], Union@@#==Range[n] && Length[Select[Tuples[#], UnsameQ@@#&]]==0&]]], {n, 0, 5}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jan 23 2024
STATUS
approved