Identifier
Values
=>
Cc0020;cc-rep-0 Cc0020;cc-rep
([],1)=>([],0)=>0 ([],2)=>([],0)=>0 ([(0,1)],2)=>([],1)=>0 ([],3)=>([],0)=>0 ([(1,2)],3)=>([],1)=>0 ([(0,2),(1,2)],3)=>([(0,1)],2)=>1 ([(0,1),(0,2),(1,2)],3)=>([(0,1),(0,2),(1,2)],3)=>2 ([],4)=>([],0)=>0 ([(2,3)],4)=>([],1)=>0 ([(1,3),(2,3)],4)=>([(0,1)],2)=>1 ([(0,3),(1,3),(2,3)],4)=>([(0,1),(0,2),(1,2)],3)=>2 ([(0,3),(1,2)],4)=>([],2)=>0 ([(0,3),(1,2),(2,3)],4)=>([(0,2),(1,2)],3)=>1 ([(1,2),(1,3),(2,3)],4)=>([(0,1),(0,2),(1,2)],3)=>2 ([(0,3),(1,2),(1,3),(2,3)],4)=>([(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>2 ([(0,2),(0,3),(1,2),(1,3)],4)=>([(0,2),(0,3),(1,2),(1,3)],4)=>2 ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)=>3 ([],5)=>([],0)=>0 ([(3,4)],5)=>([],1)=>0 ([(2,4),(3,4)],5)=>([(0,1)],2)=>1 ([(1,4),(2,4),(3,4)],5)=>([(0,1),(0,2),(1,2)],3)=>2 ([(0,4),(1,4),(2,4),(3,4)],5)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>3 ([(1,4),(2,3)],5)=>([],2)=>0 ([(1,4),(2,3),(3,4)],5)=>([(0,2),(1,2)],3)=>1 ([(0,1),(2,4),(3,4)],5)=>([(1,2)],3)=>1 ([(2,3),(2,4),(3,4)],5)=>([(0,1),(0,2),(1,2)],3)=>2 ([(0,4),(1,4),(2,3),(3,4)],5)=>([(0,3),(1,2),(1,3),(2,3)],4)=>2 ([(1,4),(2,3),(2,4),(3,4)],5)=>([(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>2 ([(1,3),(1,4),(2,3),(2,4)],5)=>([(0,2),(0,3),(1,2),(1,3)],4)=>2 ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)=>3 ([(0,4),(1,3),(2,3),(2,4)],5)=>([(0,3),(1,2),(2,3)],4)=>1 ([(0,1),(2,3),(2,4),(3,4)],5)=>([(1,2),(1,3),(2,3)],4)=>2 ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)=>([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)=>2 ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)=>([(0,3),(0,4),(1,2),(1,4),(2,3)],5)=>2 ([],6)=>([],0)=>0 ([(4,5)],6)=>([],1)=>0 ([(3,5),(4,5)],6)=>([(0,1)],2)=>1 ([(2,5),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>2 ([(1,5),(2,5),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>3 ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>4 ([(2,5),(3,4)],6)=>([],2)=>0 ([(2,5),(3,4),(4,5)],6)=>([(0,2),(1,2)],3)=>1 ([(1,2),(3,5),(4,5)],6)=>([(1,2)],3)=>1 ([(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>2 ([(1,5),(2,5),(3,4),(4,5)],6)=>([(0,3),(1,2),(1,3),(2,3)],4)=>2 ([(0,1),(2,5),(3,5),(4,5)],6)=>([(1,2),(1,3),(2,3)],4)=>2 ([(2,5),(3,4),(3,5),(4,5)],6)=>([(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>2 ([(0,5),(1,5),(2,5),(3,4),(4,5)],6)=>([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>3 ([(2,4),(2,5),(3,4),(3,5)],6)=>([(0,2),(0,3),(1,2),(1,3)],4)=>2 ([(0,5),(1,5),(2,4),(3,4)],6)=>([(0,3),(1,2)],4)=>1 ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)=>([(0,3),(1,2),(1,4),(2,4),(3,4)],5)=>2 ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)=>3 ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)=>([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)=>2 ([(0,5),(1,4),(2,3)],6)=>([],3)=>0 ([(1,5),(2,4),(3,4),(3,5)],6)=>([(0,3),(1,2),(2,3)],4)=>1 ([(0,1),(2,5),(3,4),(4,5)],6)=>([(1,3),(2,3)],4)=>1 ([(1,2),(3,4),(3,5),(4,5)],6)=>([(1,2),(1,3),(2,3)],4)=>2 ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)=>([(0,4),(1,3),(2,3),(2,4),(3,4)],5)=>2 ([(1,4),(2,3),(2,5),(3,5),(4,5)],6)=>([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)=>2 ([(0,1),(2,5),(3,4),(3,5),(4,5)],6)=>([(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>2 ([(1,4),(1,5),(2,3),(2,5),(3,4)],6)=>([(0,3),(0,4),(1,2),(1,4),(2,3)],5)=>2 ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)=>([(0,4),(1,3),(2,3),(2,4)],5)=>1 ([(0,1),(2,4),(2,5),(3,4),(3,5)],6)=>([(1,3),(1,4),(2,3),(2,4)],5)=>2 ([(0,5),(1,5),(2,3),(2,4),(3,4)],6)=>([(0,1),(2,3),(2,4),(3,4)],5)=>2 ([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5)],6)=>([(0,2),(1,4),(1,5),(2,3),(3,4),(3,5),(4,5)],6)=>2 ([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>3 ([(0,4),(1,4),(2,3),(2,5),(3,5),(4,5)],6)=>([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>2 ([(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)=>2 ([(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)=>2 ([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(4,5)],6)=>([(0,4),(0,5),(1,2),(1,3),(2,3),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>2 ([],7)=>([],0)=>0 ([(5,6)],7)=>([],1)=>0 ([(4,6),(5,6)],7)=>([(0,1)],2)=>1 ([(3,6),(4,6),(5,6)],7)=>([(0,1),(0,2),(1,2)],3)=>2 ([(2,6),(3,6),(4,6),(5,6)],7)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>3 ([(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>4 ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5 ([(3,6),(4,5)],7)=>([],2)=>0 ([(3,6),(4,5),(5,6)],7)=>([(0,2),(1,2)],3)=>1 ([(2,3),(4,6),(5,6)],7)=>([(1,2)],3)=>1 ([(4,5),(4,6),(5,6)],7)=>([(0,1),(0,2),(1,2)],3)=>2 ([(2,6),(3,6),(4,5),(5,6)],7)=>([(0,3),(1,2),(1,3),(2,3)],4)=>2 ([(1,2),(3,6),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>2 ([(3,6),(4,5),(4,6),(5,6)],7)=>([(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>2 ([(1,6),(2,6),(3,6),(4,5),(5,6)],7)=>([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>3 ([(0,1),(2,6),(3,6),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>3 ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7)=>([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 ([(3,5),(3,6),(4,5),(4,6)],7)=>([(0,2),(0,3),(1,2),(1,3)],4)=>2 ([(1,6),(2,6),(3,5),(4,5)],7)=>([(0,3),(1,2)],4)=>1 ([(1,6),(2,6),(3,4),(4,5),(5,6)],7)=>([(0,3),(1,2),(1,4),(2,4),(3,4)],5)=>2 ([(0,6),(1,6),(2,6),(3,5),(4,5)],7)=>([(0,1),(2,3),(2,4),(3,4)],5)=>2 ([(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)=>3 ([(1,6),(2,6),(3,5),(4,5),(5,6)],7)=>([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)=>2 ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7)=>([(0,1),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3 ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7)=>([(0,1),(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3 ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7)=>([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(4,5)],6)=>2 ([(1,6),(2,5),(3,4)],7)=>([],3)=>0 ([(2,6),(3,5),(4,5),(4,6)],7)=>([(0,3),(1,2),(2,3)],4)=>1 ([(1,2),(3,6),(4,5),(5,6)],7)=>([(1,3),(2,3)],4)=>1 ([(0,3),(1,2),(4,6),(5,6)],7)=>([(2,3)],4)=>1 ([(2,3),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>2 ([(1,6),(2,5),(3,4),(4,6),(5,6)],7)=>([(0,4),(1,3),(2,3),(2,4),(3,4)],5)=>2 ([(0,1),(2,6),(3,6),(4,5),(5,6)],7)=>([(1,4),(2,3),(2,4),(3,4)],5)=>2 ([(2,5),(3,4),(3,6),(4,6),(5,6)],7)=>([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)=>2 ([(1,2),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>2 ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7)=>([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3 ([(2,5),(2,6),(3,4),(3,6),(4,5)],7)=>([(0,3),(0,4),(1,2),(1,4),(2,3)],5)=>2 ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)=>([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5)],6)=>2 ([(1,6),(2,5),(3,4),(3,5),(4,6)],7)=>([(0,4),(1,3),(2,3),(2,4)],5)=>1 ([(1,2),(3,5),(3,6),(4,5),(4,6)],7)=>([(1,3),(1,4),(2,3),(2,4)],5)=>2 ([(0,6),(1,5),(2,4),(3,4),(5,6)],7)=>([(0,1),(2,4),(3,4)],5)=>1 ([(1,6),(2,6),(3,4),(3,5),(4,5)],7)=>([(0,1),(2,3),(2,4),(3,4)],5)=>2 ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>([(0,4),(1,2),(2,5),(3,4),(3,5),(4,5)],6)=>2 ([(1,5),(2,3),(2,6),(3,6),(4,5),(4,6)],7)=>([(0,2),(1,4),(1,5),(2,3),(3,4),(3,5),(4,5)],6)=>2 ([(0,6),(1,3),(2,3),(4,5),(4,6),(5,6)],7)=>([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2 ([(1,2),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>3 ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)=>([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>2 ([(1,5),(2,5),(3,4),(3,6),(4,6),(5,6)],7)=>([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>2 ([(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)=>2 ([(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)=>2 ([(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)=>2 ([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5)],7)=>([(0,1),(2,4),(2,5),(3,4),(3,5)],6)=>2 ([(0,4),(1,4),(2,5),(2,6),(3,5),(3,6),(5,6)],7)=>([(0,1),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>3 ([(0,1),(2,5),(3,4),(4,6),(5,6)],7)=>([(1,4),(2,3),(3,4)],5)=>1 ([(0,3),(1,2),(4,5),(4,6),(5,6)],7)=>([(2,3),(2,4),(3,4)],5)=>2 ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)=>([(0,5),(1,4),(2,3),(3,4),(3,5),(4,5)],6)=>2 ([(0,1),(2,3),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>2 ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)=>1 ([(0,1),(2,5),(2,6),(3,4),(3,6),(4,5)],7)=>([(1,4),(1,5),(2,3),(2,5),(3,4)],6)=>2 ([(0,6),(1,5),(2,3),(2,4),(3,4),(5,6)],7)=>([(0,5),(1,5),(2,3),(2,4),(3,4)],6)=>2 ([(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)=>2 ([(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)=>2 ([(1,2),(1,6),(2,6),(3,4),(3,5),(4,5),(5,6)],7)=>([(0,4),(0,5),(1,2),(1,3),(2,3),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>2 ([(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)=>2 ([(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)=>2 ([(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)=>2
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Description
The dimension of a graph.
The dimension of a graph is the least integer $n$ such that there exists a representation of the graph in the Euclidean space of dimension $n$ with all vertices distinct and all edges having unit length. Edges are allowed to intersect, however.
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 $G$.