OFFSET
0,4
COMMENTS
These are graphs with exactly one involution and no other symmetries.
LINKS
FORMULA
a(n) = n!/2 * A330346(n).
EXAMPLE
The a(4) = 24 graphs:
{12,13,24} {12,13,14,23}
{12,13,34} {12,13,14,24}
{12,14,23} {12,13,14,34}
{12,14,34} {12,13,23,24}
{12,23,34} {12,13,23,34}
{12,24,34} {12,14,23,24}
{13,14,23} {12,14,24,34}
{13,14,24} {12,23,24,34}
{13,23,24} {13,14,23,34}
{13,24,34} {13,14,24,34}
{14,23,24} {13,23,24,34}
{14,23,34} {14,23,24,34}
MATHEMATICA
graprms[m_]:=Union[Table[Sort[Sort/@(m/.Rule@@@Table[{p[[i]], i}, {i, Length[p]}])], {p, Permutations[Union@@m]}]];
Table[Length[Select[Subsets[Subsets[Range[n], {2}]], Union@@#==Range[n]&&Length[graprms[#]]==n!/2&]], {n, 0, 5}]
CROSSREFS
The non-covering version is A330345.
Covering simple graphs are A006129.
Covering graphs with exactly one automorphism are A330343.
Graphs with exactly two automorphisms are A330297 (labeled covering), A330344 (unlabeled), A330345 (labeled), and A330346 (unlabeled covering).
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Dec 12 2019
STATUS
approved