Identifier
Values
([(0,1)],2) => ([],1) => ([],1) => 1
([(1,2)],3) => ([],1) => ([],1) => 1
([(2,3)],4) => ([],1) => ([],1) => 1
([(0,3),(1,2)],4) => ([],2) => ([(0,1)],2) => 2
([(3,4)],5) => ([],1) => ([],1) => 1
([(1,4),(2,3)],5) => ([],2) => ([(0,1)],2) => 2
([(0,1),(2,4),(3,4)],5) => ([(1,2)],3) => ([(0,2),(1,2)],3) => 4
([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5) => ([(0,4),(1,3),(2,3),(2,4)],5) => 16
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,4)],6) => ([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6) => 8
([(0,4),(1,3),(2,3),(2,4)],5) => ([(0,3),(1,2),(2,3)],4) => ([(0,3),(1,2),(2,3)],4) => 8
([(0,3),(0,4),(1,2),(1,4),(2,3)],5) => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5) => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5) => 5
([(4,5)],6) => ([],1) => ([],1) => 1
([(2,5),(3,4)],6) => ([],2) => ([(0,1)],2) => 2
([(1,2),(3,5),(4,5)],6) => ([(1,2)],3) => ([(0,2),(1,2)],3) => 4
([(0,5),(1,5),(2,4),(3,4)],6) => ([(0,3),(1,2)],4) => ([(0,2),(0,3),(1,2),(1,3)],4) => 4
([(1,5),(2,3),(2,4),(3,5),(4,5)],6) => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5) => ([(0,4),(1,3),(2,3),(2,4)],5) => 16
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,4)],6) => ([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6) => 8
([(0,5),(1,4),(2,3)],6) => ([],3) => ([(0,1),(0,2),(1,2)],3) => 3
([(1,5),(2,4),(3,4),(3,5)],6) => ([(0,3),(1,2),(2,3)],4) => ([(0,3),(1,2),(2,3)],4) => 8
([(1,4),(1,5),(2,3),(2,5),(3,4)],6) => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5) => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5) => 5
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,5),(0,6),(1,2),(1,4),(1,6),(2,3),(2,6),(3,4),(3,5),(4,5)],7) => ([(0,1),(0,4),(0,5),(1,2),(1,3),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7) => 7
([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6) => ([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6) => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,4)],6) => 6
([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6) => ([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6) => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 6
([(5,6)],7) => ([],1) => ([],1) => 1
([(3,6),(4,5)],7) => ([],2) => ([(0,1)],2) => 2
([(2,3),(4,6),(5,6)],7) => ([(1,2)],3) => ([(0,2),(1,2)],3) => 4
([(1,6),(2,6),(3,5),(4,5)],7) => ([(0,3),(1,2)],4) => ([(0,2),(0,3),(1,2),(1,3)],4) => 4
([(2,6),(3,4),(3,5),(4,6),(5,6)],7) => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5) => ([(0,4),(1,3),(2,3),(2,4)],5) => 16
([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,4)],6) => ([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6) => 8
([(1,6),(2,5),(3,4)],7) => ([],3) => ([(0,1),(0,2),(1,2)],3) => 3
([(2,6),(3,5),(4,5),(4,6)],7) => ([(0,3),(1,2),(2,3)],4) => ([(0,3),(1,2),(2,3)],4) => 8
([(2,5),(2,6),(3,4),(3,6),(4,5)],7) => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5) => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5) => 5
([(0,6),(1,6),(2,6),(3,4),(3,5),(4,5)],7) => ([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6) => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 6
([(1,2),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7) => ([(0,5),(0,6),(1,2),(1,4),(1,6),(2,3),(2,6),(3,4),(3,5),(4,5)],7) => ([(0,1),(0,4),(0,5),(1,2),(1,3),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7) => 7
([(0,6),(1,5),(2,3),(2,5),(3,6),(4,5),(4,6)],7) => ([(0,4),(0,6),(1,3),(1,5),(2,5),(2,6),(3,4),(3,5),(4,6)],7) => ([(0,1),(0,3),(0,5),(1,2),(1,4),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => 7
([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5)],7) => ([(0,6),(1,4),(1,5),(2,3),(2,5),(2,6),(3,4),(3,6),(4,5)],7) => ([(0,2),(0,4),(0,6),(1,2),(1,3),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 7
([(0,1),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => ([(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,6),(4,5)],7) => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7) => 7
([(0,6),(1,6),(2,3),(2,5),(3,5),(4,5),(4,6)],7) => ([(0,4),(0,5),(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5)],7) => ([(0,1),(0,2),(0,6),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(3,6),(4,6),(5,6)],7) => 7
([(1,5),(1,6),(2,3),(2,4),(3,6),(4,5)],7) => ([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6) => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,4)],6) => 6
([(0,6),(1,2),(1,3),(2,5),(3,4),(4,6),(5,6)],7) => ([(0,1),(0,3),(1,2),(2,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(0,4),(0,5),(0,6),(1,3),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(4,6)],7) => 7
([(0,5),(1,2),(1,3),(2,6),(3,6),(4,5),(4,6)],7) => ([(0,3),(1,2),(1,5),(2,4),(3,6),(4,5),(4,6),(5,6)],7) => ([(0,3),(0,4),(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 7
([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => ([(0,1),(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
([(0,1),(2,5),(2,6),(3,4),(3,6),(4,5)],7) => ([(1,4),(1,5),(2,3),(2,5),(3,4)],6) => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => 6
([(0,6),(1,5),(2,3),(2,4),(3,4),(5,6)],7) => ([(0,5),(1,5),(2,3),(2,4),(3,4)],6) => ([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
([(0,5),(1,2),(1,4),(2,3),(3,6),(4,6),(5,6)],7) => ([(0,6),(1,2),(1,3),(2,5),(3,4),(4,5),(4,6),(5,6)],7) => ([(0,3),(0,5),(0,6),(1,3),(1,4),(1,6),(2,3),(2,4),(2,5),(3,6),(4,5),(4,6),(5,6)],7) => 7
([(0,5),(1,4),(1,5),(2,3),(2,6),(3,6),(4,6)],7) => ([(0,3),(1,3),(1,4),(2,5),(2,6),(4,5),(4,6),(5,6)],7) => ([(0,3),(0,4),(0,6),(1,3),(1,4),(1,6),(2,3),(2,5),(2,6),(3,5),(4,5),(4,6),(5,6)],7) => 7
([(1,5),(1,6),(2,3),(2,4),(3,4),(5,6)],7) => ([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6) => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 6
([(0,6),(1,2),(1,3),(2,3),(4,5),(4,6),(5,6)],7) => ([(0,1),(0,2),(1,2),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 7
([(0,5),(0,6),(1,2),(1,4),(2,3),(3,5),(4,6)],7) => ([(0,5),(0,6),(1,2),(1,4),(2,3),(3,5),(4,6)],7) => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,5),(4,6)],7) => 7
([(0,5),(0,6),(1,2),(1,3),(2,3),(4,5),(4,6)],7) => ([(0,5),(0,6),(1,2),(1,3),(2,3),(4,5),(4,6)],7) => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 7
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Description
The pebbling number of a connected graph.
Map
line graph
Description
The line graph of a graph.
Let $G$ be a graph with edge set $E$. Then its line graph is the graph with vertex set $E$, such that two vertices $e$ and $f$ are adjacent if and only if they are incident to a common vertex in $G$.
Let $G$ be a graph with edge set $E$. Then its line graph is the graph with vertex set $E$, such that two vertices $e$ and $f$ are adjacent if and only if they are incident to a common vertex in $G$.
Map
complement
Description
The complement of a graph.
The complement of a graph has the same vertices, but exactly those edges that are not in the original graph.
The complement of a graph has the same vertices, but exactly those edges that are not in the original graph.
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