- FindStat

Identifier

Mp00074: Posets —to graph⟶ Graphs
Mp00264: Graphs —delete endpoints⟶ Graphs
St001545: Graphs ⟶ ℤ

Values

([(0,1),(0,2),(1,3),(2,3)],4) => ([(0,2),(0,3),(1,2),(1,3)],4) => ([(0,2),(0,3),(1,2),(1,3)],4) => 12

([(0,2),(0,3),(1,2),(1,3)],4) => ([(0,2),(0,3),(1,2),(1,3)],4) => ([(0,2),(0,3),(1,2),(1,3)],4) => 12

([(0,1),(0,2),(0,3),(2,4),(3,4)],5) => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => ([(0,2),(0,3),(1,2),(1,3)],4) => 12

([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5) => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 26

([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => ([(0,2),(0,3),(1,2),(1,3)],4) => 12

([(0,2),(0,3),(2,4),(3,1),(3,4)],5) => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => ([(0,2),(0,3),(1,2),(1,3)],4) => 12

([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5) => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 26

([(0,4),(1,3),(1,4),(2,3),(2,4)],5) => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => ([(0,2),(0,3),(1,2),(1,3)],4) => 12

([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 26

([(0,3),(1,2),(1,3),(2,4),(3,4)],5) => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => ([(0,2),(0,3),(1,2),(1,3)],4) => 12

([(0,3),(0,4),(1,3),(1,4),(4,2)],5) => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => ([(0,2),(0,3),(1,2),(1,3)],4) => 12

([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5) => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 26

([(0,2),(0,3),(1,4),(2,4),(3,1)],5) => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5) => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5) => 20

([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => ([(0,2),(0,3),(1,2),(1,3)],4) => 12

([(0,3),(0,4),(1,2),(1,3),(1,4)],5) => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => ([(0,2),(0,3),(1,2),(1,3)],4) => 12

([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5) => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 26

([(0,3),(0,4),(1,2),(1,3),(2,4)],5) => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5) => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5) => 20

([(0,3),(0,4),(1,2),(2,3),(2,4)],5) => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => ([(0,2),(0,3),(1,2),(1,3)],4) => 12

([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => ([(0,2),(0,3),(1,2),(1,3)],4) => 12

([(0,1),(0,2),(0,3),(0,4),(3,5),(4,5)],6) => ([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6) => ([(0,2),(0,3),(1,2),(1,3)],4) => 12

([(0,1),(0,2),(0,3),(0,4),(2,5),(3,5),(4,5)],6) => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 26

([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6) => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 26

([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1)],6) => ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6) => ([(0,2),(0,3),(1,2),(1,3)],4) => 12

([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1),(4,5)],6) => ([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 26

([(0,2),(0,3),(0,4),(3,5),(4,5),(5,1)],6) => ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,2),(0,3),(1,2),(1,3)],4) => 12

([(0,2),(0,3),(0,4),(3,5),(4,1),(4,5)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => ([(0,2),(0,3),(1,2),(1,3)],4) => 12

([(0,1),(0,2),(0,3),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 26

([(0,3),(0,4),(3,5),(4,5),(5,1),(5,2)],6) => ([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6) => ([(0,2),(0,3),(1,2),(1,3)],4) => 12

([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(5,1)],6) => ([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 26

([(0,3),(0,4),(3,5),(4,1),(4,5),(5,2)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => ([(0,2),(0,3),(1,2),(1,3)],4) => 12

([(0,3),(0,4),(3,5),(4,1),(4,2),(4,5)],6) => ([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6) => ([(0,2),(0,3),(1,2),(1,3)],4) => 12

([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,2),(0,3),(1,2),(1,3)],4) => 12

([(0,2),(0,3),(2,4),(2,5),(3,1),(3,4),(3,5)],6) => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 26

([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6) => ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,2),(0,3),(1,2),(1,3)],4) => 12

([(0,5),(1,4),(1,5),(2,4),(2,5),(4,3)],6) => ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,2),(0,3),(1,2),(1,3)],4) => 12

([(0,5),(1,3),(1,5),(2,3),(2,5),(3,4),(5,4)],6) => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 26

([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(5,3)],6) => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 26

([(0,5),(1,4),(1,5),(2,4),(2,5),(5,3)],6) => ([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6) => ([(0,2),(0,3),(1,2),(1,3)],4) => 12

([(0,5),(1,5),(2,3),(2,5),(3,4),(5,4)],6) => ([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6) => ([(0,2),(0,3),(1,2),(1,3)],4) => 12

([(0,3),(1,3),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6) => ([(0,2),(0,3),(1,2),(1,3)],4) => 12

([(0,3),(0,4),(1,5),(2,5),(4,1),(4,2)],6) => ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6) => ([(0,2),(0,3),(1,2),(1,3)],4) => 12

([(0,5),(1,3),(1,4),(2,5),(3,5),(4,2)],6) => ([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6) => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5) => 20

([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6) => ([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6) => ([(0,2),(0,3),(1,2),(1,3)],4) => 12

([(0,4),(2,5),(3,5),(4,1),(4,2),(4,3)],6) => ([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6) => ([(0,2),(0,3),(1,2),(1,3)],4) => 12

([(0,5),(1,4),(2,5),(3,5),(4,2),(4,3)],6) => ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,2),(0,3),(1,2),(1,3)],4) => 12

([(0,4),(1,5),(2,5),(3,5),(4,1),(4,2),(4,3)],6) => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 26

([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6) => ([(0,2),(0,3),(1,2),(1,3)],4) => 12

([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,2),(0,3),(1,2),(1,3)],4) => 12

([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 26

([(0,4),(1,4),(2,5),(3,5),(4,2),(4,3)],6) => ([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6) => ([(0,2),(0,3),(1,2),(1,3)],4) => 12

([(0,4),(1,2),(1,4),(2,3),(2,5),(4,5)],6) => ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,2),(0,3),(1,2),(1,3)],4) => 12

([(0,5),(1,2),(1,5),(2,3),(2,4),(5,3),(5,4)],6) => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 26

([(0,4),(1,2),(1,4),(2,5),(4,5),(5,3)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => ([(0,2),(0,3),(1,2),(1,3)],4) => 12

([(0,4),(1,2),(1,4),(2,5),(4,3),(4,5)],6) => ([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6) => ([(0,2),(0,3),(1,2),(1,3)],4) => 12

([(0,4),(0,5),(1,4),(1,5),(5,2),(5,3)],6) => ([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6) => ([(0,2),(0,3),(1,2),(1,3)],4) => 12

([(0,4),(0,5),(1,4),(1,5),(4,3),(5,2)],6) => ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,2),(0,3),(1,2),(1,3)],4) => 12

([(0,4),(0,5),(1,4),(1,5),(4,3),(5,2),(5,3)],6) => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 26

([(0,4),(0,5),(1,4),(1,5),(2,3),(5,2)],6) => ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6) => ([(0,2),(0,3),(1,2),(1,3)],4) => 12

([(0,4),(0,5),(1,4),(1,5),(3,2),(4,3),(5,3)],6) => ([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 26

([(0,5),(1,3),(1,4),(2,3),(2,4),(4,5)],6) => ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6) => ([(0,2),(0,3),(1,2),(1,3)],4) => 12

([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => ([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 26

([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5)],6) => ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6) => ([(0,2),(0,3),(1,2),(1,3)],4) => 12

([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => ([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 26

([(0,4),(0,5),(1,4),(1,5),(2,3),(3,5)],6) => ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6) => ([(0,2),(0,3),(1,2),(1,3)],4) => 12

([(0,4),(0,5),(1,4),(1,5),(2,3),(3,4),(3,5)],6) => ([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 26

([(0,4),(1,2),(1,3),(1,4),(3,5),(4,5)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => ([(0,2),(0,3),(1,2),(1,3)],4) => 12

([(0,4),(1,2),(1,3),(1,4),(2,5),(3,5)],6) => ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6) => ([(0,2),(0,3),(1,2),(1,3)],4) => 12

([(0,4),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6) => ([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 26

([(0,2),(0,3),(0,4),(1,5),(3,5),(4,1)],6) => ([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6) => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5) => 20

([(0,5),(1,2),(1,3),(1,4),(3,5),(4,5)],6) => ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,2),(0,3),(1,2),(1,3)],4) => 12

([(0,5),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6) => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 26

([(0,3),(1,2),(1,4),(1,5),(3,4),(3,5)],6) => ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,2),(0,3),(1,2),(1,3)],4) => 12

([(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 26

([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6) => ([(0,2),(0,3),(1,2),(1,3)],4) => 12

([(0,3),(0,4),(2,5),(3,2),(4,1),(4,5)],6) => ([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6) => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5) => 20

([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6) => ([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6) => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5) => 20

([(0,5),(1,2),(1,3),(2,5),(3,5),(5,4)],6) => ([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6) => ([(0,2),(0,3),(1,2),(1,3)],4) => 12

([(0,4),(1,2),(1,3),(2,5),(3,4),(3,5)],6) => ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6) => ([(0,2),(0,3),(1,2),(1,3)],4) => 12

([(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 26

([(0,4),(1,2),(1,3),(2,5),(3,4),(4,5)],6) => ([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6) => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5) => 20

([(0,3),(0,4),(2,5),(3,5),(4,1),(4,2)],6) => ([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6) => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5) => 20

([(0,5),(1,3),(1,4),(3,5),(4,2),(4,5)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => ([(0,2),(0,3),(1,2),(1,3)],4) => 12

([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6) => ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6) => ([(0,2),(0,3),(1,2),(1,3)],4) => 12

([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6) => ([(0,2),(0,3),(1,2),(1,3)],4) => 12

([(0,4),(1,2),(1,3),(2,5),(3,5),(5,4)],6) => ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6) => ([(0,2),(0,3),(1,2),(1,3)],4) => 12

([(0,4),(0,5),(1,3),(1,4),(1,5),(5,2)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => ([(0,2),(0,3),(1,2),(1,3)],4) => 12

([(0,4),(0,5),(1,2),(1,4),(1,5),(4,3),(5,3)],6) => ([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 26

([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(5,2)],6) => ([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 26

([(0,4),(0,5),(1,2),(1,4),(1,5),(2,3)],6) => ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6) => ([(0,2),(0,3),(1,2),(1,3)],4) => 12

([(0,4),(0,5),(1,2),(1,4),(2,5),(4,3)],6) => ([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6) => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5) => 20

([(0,4),(0,5),(1,2),(1,4),(2,5),(5,3)],6) => ([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6) => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5) => 20

([(0,2),(0,4),(1,3),(1,4),(3,5),(4,5)],6) => ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6) => ([(0,2),(0,3),(1,2),(1,3)],4) => 12

([(0,4),(0,5),(1,2),(1,4),(2,3),(2,5)],6) => ([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6) => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5) => 20

([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5)],6) => ([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6) => ([(0,2),(0,3),(1,2),(1,3)],4) => 12

([(0,4),(0,5),(1,2),(1,3),(1,4),(3,5)],6) => ([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6) => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5) => 20

([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5)],6) => ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,2),(0,3),(1,2),(1,3)],4) => 12

([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5)],6) => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 26

([(0,3),(0,4),(1,2),(1,4),(1,5),(3,5)],6) => ([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6) => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5) => 20

([(0,4),(0,5),(1,2),(1,3),(3,4),(3,5)],6) => ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6) => ([(0,2),(0,3),(1,2),(1,3)],4) => 12

([(0,2),(0,4),(2,5),(3,1),(3,5),(4,3)],6) => ([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6) => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5) => 20

([(0,4),(0,5),(1,2),(1,3),(2,5),(3,5)],6) => ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6) => ([(0,2),(0,3),(1,2),(1,3)],4) => 12

>>> Load all 753 entries. <<<

search for individual values

searching the database for the individual values of this statistic

Description

The second Elser number of a connected graph.
For a connected graph $G$ the $k$-th Elser number is
$$ els_k(G) = (-1)^{|V(G)|+1} \sum_N (-1)^{|E(N)|} |V(N)|^k $$
where the sum is over all nuclei of $G$, that is, the connected subgraphs of $G$ whose vertex set is a vertex cover of $G$.
It is clear that this number is even. It was shown in [1] that it is non-negative.

Map

delete endpoints

Description

Sends a graph to a maximal subgraph with no endpoints.
An endpoint of a graph is a vertex of degree one. Given an arbitrary graph, this map repeatedly searches for an endpoint and deletes it, until no endpoint remains. The result does not depend on the order of endpoints chosen, up to isomorphism. The map preserves the number of connected components. For a connected graph with at least one cycle, this map returns the 2-core.

Map

to graph

Description

Returns the Hasse diagram of the poset as an undirected graph.