A326279 Number of labeled n-vertex simple graphs containing either a crossing or a nesting pair of edges.

0, 0, 0, 0, 28, 864, 32064, 2094064

Offset: 0

Author

Gus Wiseman, Jun 23 2019

Keywords

• nonn
• more

Comments

Two edges {a,b}, {c,d} are crossing if a < c < b < d or c < a < d < b, and nesting if a < c < d < b or c < a < b < d.

Examples

			The a(4) = 28 edge-sets:
  {13,24}  {12,13,24}  {12,13,14,23}  {12,13,14,23,24}  {12,13,14,23,24,34}
  {14,23}  {12,14,23}  {12,13,14,24}  {12,13,14,23,34}
           {13,14,23}  {12,13,23,24}  {12,13,14,24,34}
           {13,14,24}  {12,13,24,34}  {12,13,23,24,34}
           {13,23,24}  {12,14,23,24}  {12,14,23,24,34}
           {13,24,34}  {12,14,23,34}  {13,14,23,24,34}
           {14,23,24}  {13,14,23,24}
           {14,23,34}  {13,14,23,34}
                       {13,14,24,34}
                       {13,23,24,34}
                       {14,23,24,34}
		

Crossrefs

Crossing and nesting simple graphs are (both) A326210, while non-crossing, non-nesting simple graphs are A326244.

Cf. A000108, A001519, A006125, A016098, A054726, A095661, A324170.

Cf. A326209, A326211, A326248, A326250, A326256.

Programs

Mathematica

croXQ[stn_]:=MatchQ[stn,{_,{x_,y_},_,{z_,t_},_}/;x_,{x_,y_},_,{z_,t_},_}/;x
				

Formula

A006125(n) = a(n) + A326244(n).