Identifier
Values
([(0,1)],2) => ([(0,1)],2) => ([],1) => 0
([(1,2)],3) => ([(1,2)],3) => ([],1) => 0
([(0,2),(1,2)],3) => ([(0,2),(1,2)],3) => ([(0,1)],2) => 1
([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(1,2)],3) => 2
([(2,3)],4) => ([(2,3)],4) => ([],1) => 0
([(1,3),(2,3)],4) => ([(1,3),(2,3)],4) => ([(0,1)],2) => 1
([(0,3),(1,3),(2,3)],4) => ([(0,3),(1,3),(2,3)],4) => ([(0,1),(0,2),(1,2)],3) => 2
([(0,3),(1,2)],4) => ([(0,3),(1,2)],4) => ([],2) => 0
([(1,2),(1,3),(2,3)],4) => ([(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(1,2)],3) => 2
([(0,2),(0,3),(1,2),(1,3)],4) => ([(0,1),(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
([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => ([(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
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => ([(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) => ([(3,4)],5) => ([],1) => 0
([(2,4),(3,4)],5) => ([(2,4),(3,4)],5) => ([(0,1)],2) => 1
([(1,4),(2,4),(3,4)],5) => ([(1,4),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,2)],3) => 2
([(0,4),(1,4),(2,4),(3,4)],5) => ([(0,4),(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) => ([(1,4),(2,3)],5) => ([],2) => 0
([(0,1),(2,4),(3,4)],5) => ([(0,1),(2,4),(3,4)],5) => ([(1,2)],3) => 1
([(2,3),(2,4),(3,4)],5) => ([(2,3),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,2)],3) => 2
([(1,3),(1,4),(2,3),(2,4)],5) => ([(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
([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(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
([(0,1),(2,3),(2,4),(3,4)],5) => ([(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) => ([(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) => ([(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) => ([(4,5)],6) => ([],1) => 0
([(3,5),(4,5)],6) => ([(3,5),(4,5)],6) => ([(0,1)],2) => 1
([(2,5),(3,5),(4,5)],6) => ([(2,5),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => 2
([(1,5),(2,5),(3,5),(4,5)],6) => ([(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) => ([(0,5),(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) => ([(2,5),(3,4)],6) => ([],2) => 0
([(1,2),(3,5),(4,5)],6) => ([(1,2),(3,5),(4,5)],6) => ([(1,2)],3) => 1
([(3,4),(3,5),(4,5)],6) => ([(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => 2
([(0,1),(2,5),(3,5),(4,5)],6) => ([(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) => ([(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
([(0,5),(1,5),(2,4),(3,4)],6) => ([(0,5),(1,5),(2,4),(3,4)],6) => ([(0,3),(1,2)],4) => 1
([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(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
([(0,5),(1,4),(2,3)],6) => ([(0,5),(1,4),(2,3)],6) => ([],3) => 0
([(1,2),(3,4),(3,5),(4,5)],6) => ([(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) => ([(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) => ([(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
([(0,5),(1,5),(2,3),(2,4),(3,4)],6) => ([(0,5),(1,5),(2,3),(2,4),(3,4)],6) => ([(0,1),(2,3),(2,4),(3,4)],5) => 2
([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(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
([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(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) => ([(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) => ([(0,3),(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) => ([(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) => ([(0,1),(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) => ([(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) => ([(5,6)],7) => ([],1) => 0
([(4,6),(5,6)],7) => ([(4,6),(5,6)],7) => ([(0,1)],2) => 1
([(3,6),(4,6),(5,6)],7) => ([(3,6),(4,6),(5,6)],7) => ([(0,1),(0,2),(1,2)],3) => 2
([(2,6),(3,6),(4,6),(5,6)],7) => ([(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) => ([(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) => ([(0,6),(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) => ([(3,6),(4,5)],7) => ([],2) => 0
([(2,3),(4,6),(5,6)],7) => ([(2,3),(4,6),(5,6)],7) => ([(1,2)],3) => 1
([(4,5),(4,6),(5,6)],7) => ([(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),(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) => ([(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) => ([(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
([(1,6),(2,6),(3,5),(4,5)],7) => ([(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) => ([(0,6),(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) => ([(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
([(1,6),(2,5),(3,4)],7) => ([(1,6),(2,5),(3,4)],7) => ([],3) => 0
([(0,3),(1,2),(4,6),(5,6)],7) => ([(0,3),(1,2),(4,6),(5,6)],7) => ([(2,3)],4) => 1
([(2,3),(4,5),(4,6),(5,6)],7) => ([(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) => ([(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) => ([(1,2),(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
([(1,6),(2,6),(3,4),(3,5),(4,5)],7) => ([(1,6),(2,6),(3,4),(3,5),(4,5)],7) => ([(0,1),(2,3),(2,4),(3,4)],5) => 2
([(1,2),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(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
([(0,6),(1,6),(2,6),(3,4),(3,5),(4,5)],7) => ([(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) => ([(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
([(1,5),(1,6),(2,3),(2,4),(3,6),(4,5)],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) => 2
([(1,4),(1,6),(2,3),(2,6),(3,5),(4,5),(5,6)],7) => ([(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
([(0,3),(1,2),(4,5),(4,6),(5,6)],7) => ([(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) => ([(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) => ([(0,6),(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) => ([(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) => ([(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) => ([(1,2),(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) => ([(0,5),(0,6),(1,2),(1,4),(2,3),(3,5),(4,6)],7) => 2
search for individual values
searching the database for the individual values of this statistic
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 $G$.
Map
Ore closure
Description
The Ore closure of a graph.
The Ore closure of a connected graph $G$ has the same vertices as $G$, and the smallest set of edges containing the edges of $G$ such that for any two vertices $u$ and $v$ whose sum of degrees is at least the number of vertices, then $(u,v)$ is also an edge.
For disconnected graphs, we compute the closure separately for each component.
The Ore closure of a connected graph $G$ has the same vertices as $G$, and the smallest set of edges containing the edges of $G$ such that for any two vertices $u$ and $v$ whose sum of degrees is at least the number of vertices, then $(u,v)$ is also an edge.
For disconnected graphs, we compute the closure separately for each component.
searching the database
Sorry, this statistic was not found in the database
or
add this statistic to the database – it's very simple and we need your support!