Values
([(0,1)],2) => ([],1) => 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
([(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
([(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(1,2)],3) => 2
([(0,2),(0,3),(1,2),(1,3)],4) => ([(0,2),(0,3),(1,2),(1,3)],4) => 2
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 4
([(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
([(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
([(1,3),(1,4),(2,3),(2,4)],5) => ([(0,2),(0,3),(1,2),(1,3)],4) => 2
([(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) => 3
([(0,1),(2,3),(2,4),(3,4)],5) => ([(1,2),(1,3),(2,3)],4) => 2
([(0,3),(0,4),(1,2),(1,4),(2,3)],5) => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5) => 2
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 4
([(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
([(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
([(0,1),(2,5),(3,5),(4,5)],6) => ([(1,2),(1,3),(2,3)],4) => 2
([(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
([(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) => 3
([(0,5),(1,4),(2,3)],6) => ([],3) => 0
([(1,2),(3,4),(3,5),(4,5)],6) => ([(1,2),(1,3),(2,3)],4) => 2
([(1,4),(1,5),(2,3),(2,5),(3,4)],6) => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5) => 2
([(0,1),(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
([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 4
([(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
([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6) => ([(0,4),(0,5),(1,2),(1,3),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7) => 3
([(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) => 3
([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 4
([(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
([(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
([(1,2),(3,6),(4,6),(5,6)],7) => ([(1,2),(1,3),(2,3)],4) => 2
([(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
([(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
([(0,6),(1,6),(2,6),(3,5),(4,5)],7) => ([(0,1),(2,3),(2,4),(3,4)],5) => 2
([(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) => 3
([(1,6),(2,5),(3,4)],7) => ([],3) => 0
([(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
([(2,5),(2,6),(3,4),(3,6),(4,5)],7) => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5) => 2
([(1,2),(3,5),(3,6),(4,5),(4,6)],7) => ([(1,3),(1,4),(2,3),(2,4)],5) => 2
([(1,6),(2,6),(3,4),(3,5),(4,5)],7) => ([(0,1),(2,3),(2,4),(3,4)],5) => 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
([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 4
([(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) => 3
([(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
([(1,4),(1,6),(2,3),(2,6),(3,5),(4,5),(5,6)],7) => ([(0,4),(0,5),(1,2),(1,3),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7) => 3
([(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
([(0,3),(1,2),(4,5),(4,6),(5,6)],7) => ([(2,3),(2,4),(3,4)],5) => 2
([(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
([(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) => 3
([(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 4
([(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 largest eigenvalue of a graph if it is integral.
If a graph is $d$-regular, then its largest eigenvalue equals $d$. One can show that the largest eigenvalue always lies between the average degree and the maximal degree.
This statistic is undefined if the largest eigenvalue of the graph is not integral.
If a graph is $d$-regular, then its largest eigenvalue equals $d$. One can show that the largest eigenvalue always lies between the average degree and the maximal degree.
This statistic is undefined if the largest eigenvalue of the graph is not integral.
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 $G$.
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