OFFSET
0,7
COMMENTS
These are graphs with n vertices and n edges having at least two cycles in the same component.
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..50
EXAMPLE
The a(0) = 0 through a(6) = 7 simple graphs:
. . . . . {{12}{13}{14}{23}{24}} {{12}{13}{14}{15}{23}{24}}
{{12}{13}{14}{15}{23}{45}}
{{12}{13}{14}{23}{24}{34}}
{{12}{13}{14}{23}{24}{35}}
{{12}{13}{14}{23}{24}{56}}
{{12}{13}{14}{23}{25}{45}}
{{12}{13}{14}{25}{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}], {n}], Select[Tuples[#], UnsameQ@@#&]=={}&]]], {n, 0, 5}]
CROSSREFS
For labeled set-systems we have A368600.
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jan 22 2024
EXTENSIONS
a(25) onwards from Andrew Howroyd, Feb 02 2024
STATUS
approved