Identifier
Values
([(0,1)],2) => ([(0,1)],2) => ([(0,1)],2) => ([],1) => 1
([(1,2)],3) => ([(1,2)],3) => ([(1,2)],3) => ([],1) => 1
([(0,2),(1,2)],3) => ([(0,2),(1,2)],3) => ([(0,2),(1,2)],3) => ([(0,1)],2) => 2
([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(1,2)],3) => 3
([(2,3)],4) => ([(2,3)],4) => ([(2,3)],4) => ([],1) => 1
([(1,3),(2,3)],4) => ([(1,3),(2,3)],4) => ([(1,3),(2,3)],4) => ([(0,1)],2) => 2
([(0,3),(1,3),(2,3)],4) => ([(0,3),(1,3),(2,3)],4) => ([(0,3),(1,3),(2,3)],4) => ([(0,1),(0,2),(1,2)],3) => 3
([(0,3),(1,2)],4) => ([(0,3),(1,2)],4) => ([(0,3),(1,2)],4) => ([],2) => 1
([(0,3),(1,2),(2,3)],4) => ([(0,3),(1,2),(2,3)],4) => ([(0,3),(1,2),(2,3)],4) => ([(0,2),(1,2)],3) => 2
([(1,2),(1,3),(2,3)],4) => ([(1,2),(1,3),(2,3)],4) => ([(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(1,2)],3) => 3
([(3,4)],5) => ([(3,4)],5) => ([(3,4)],5) => ([],1) => 1
([(2,4),(3,4)],5) => ([(2,4),(3,4)],5) => ([(2,4),(3,4)],5) => ([(0,1)],2) => 2
([(1,4),(2,4),(3,4)],5) => ([(1,4),(2,4),(3,4)],5) => ([(1,4),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,2)],3) => 3
([(0,4),(1,4),(2,4),(3,4)],5) => ([(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) => 4
([(1,4),(2,3)],5) => ([(1,4),(2,3)],5) => ([(1,4),(2,3)],5) => ([],2) => 1
([(1,4),(2,3),(3,4)],5) => ([(1,4),(2,3),(3,4)],5) => ([(1,4),(2,3),(3,4)],5) => ([(0,2),(1,2)],3) => 2
([(0,1),(2,4),(3,4)],5) => ([(0,1),(2,4),(3,4)],5) => ([(0,1),(2,4),(3,4)],5) => ([(1,2)],3) => 2
([(2,3),(2,4),(3,4)],5) => ([(2,3),(2,4),(3,4)],5) => ([(2,3),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,2)],3) => 3
([(0,1),(2,3),(2,4),(3,4)],5) => ([(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) => 3
([(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) => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5) => 2
([(4,5)],6) => ([(4,5)],6) => ([(4,5)],6) => ([],1) => 1
([(3,5),(4,5)],6) => ([(3,5),(4,5)],6) => ([(3,5),(4,5)],6) => ([(0,1)],2) => 2
([(2,5),(3,5),(4,5)],6) => ([(2,5),(3,5),(4,5)],6) => ([(2,5),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => 3
([(1,5),(2,5),(3,5),(4,5)],6) => ([(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) => 4
([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => ([(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) => 5
([(2,5),(3,4)],6) => ([(2,5),(3,4)],6) => ([(2,5),(3,4)],6) => ([],2) => 1
([(2,5),(3,4),(4,5)],6) => ([(2,5),(3,4),(4,5)],6) => ([(2,5),(3,4),(4,5)],6) => ([(0,2),(1,2)],3) => 2
([(1,2),(3,5),(4,5)],6) => ([(1,2),(3,5),(4,5)],6) => ([(1,2),(3,5),(4,5)],6) => ([(1,2)],3) => 2
([(3,4),(3,5),(4,5)],6) => ([(3,4),(3,5),(4,5)],6) => ([(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => 3
([(0,1),(2,5),(3,5),(4,5)],6) => ([(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) => 3
([(0,5),(1,5),(2,4),(3,4)],6) => ([(0,5),(1,5),(2,4),(3,4)],6) => ([(0,5),(1,5),(2,4),(3,4)],6) => ([(0,3),(1,2)],4) => 2
([(0,5),(1,4),(2,3)],6) => ([(0,5),(1,4),(2,3)],6) => ([(0,5),(1,4),(2,3)],6) => ([],3) => 1
([(0,1),(2,5),(3,4),(4,5)],6) => ([(0,1),(2,5),(3,4),(4,5)],6) => ([(0,1),(2,5),(3,4),(4,5)],6) => ([(1,3),(2,3)],4) => 2
([(1,2),(3,4),(3,5),(4,5)],6) => ([(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) => 3
([(1,4),(1,5),(2,3),(2,5),(3,4)],6) => ([(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
([(0,5),(1,5),(2,3),(2,4),(3,4)],6) => ([(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) => 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) => ([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6) => 3
([(5,6)],7) => ([(5,6)],7) => ([(5,6)],7) => ([],1) => 1
([(4,6),(5,6)],7) => ([(4,6),(5,6)],7) => ([(4,6),(5,6)],7) => ([(0,1)],2) => 2
([(3,6),(4,6),(5,6)],7) => ([(3,6),(4,6),(5,6)],7) => ([(3,6),(4,6),(5,6)],7) => ([(0,1),(0,2),(1,2)],3) => 3
([(2,6),(3,6),(4,6),(5,6)],7) => ([(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) => 4
([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => ([(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) => 5
([(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) => ([(0,6),(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) => 6
([(3,6),(4,5)],7) => ([(3,6),(4,5)],7) => ([(3,6),(4,5)],7) => ([],2) => 1
([(3,6),(4,5),(5,6)],7) => ([(3,6),(4,5),(5,6)],7) => ([(3,6),(4,5),(5,6)],7) => ([(0,2),(1,2)],3) => 2
([(2,3),(4,6),(5,6)],7) => ([(2,3),(4,6),(5,6)],7) => ([(2,3),(4,6),(5,6)],7) => ([(1,2)],3) => 2
([(4,5),(4,6),(5,6)],7) => ([(4,5),(4,6),(5,6)],7) => ([(4,5),(4,6),(5,6)],7) => ([(0,1),(0,2),(1,2)],3) => 3
([(1,2),(3,6),(4,6),(5,6)],7) => ([(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) => 3
([(0,1),(2,6),(3,6),(4,6),(5,6)],7) => ([(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) => 4
([(1,6),(2,6),(3,5),(4,5)],7) => ([(1,6),(2,6),(3,5),(4,5)],7) => ([(1,6),(2,6),(3,5),(4,5)],7) => ([(0,3),(1,2)],4) => 2
([(0,6),(1,6),(2,6),(3,5),(4,5)],7) => ([(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) => 3
([(1,6),(2,5),(3,4)],7) => ([(1,6),(2,5),(3,4)],7) => ([(1,6),(2,5),(3,4)],7) => ([],3) => 1
([(1,2),(3,6),(4,5),(5,6)],7) => ([(1,2),(3,6),(4,5),(5,6)],7) => ([(1,2),(3,6),(4,5),(5,6)],7) => ([(1,3),(2,3)],4) => 2
([(0,3),(1,2),(4,6),(5,6)],7) => ([(0,3),(1,2),(4,6),(5,6)],7) => ([(0,3),(1,2),(4,6),(5,6)],7) => ([(2,3)],4) => 2
([(2,3),(4,5),(4,6),(5,6)],7) => ([(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) => 3
([(2,5),(2,6),(3,4),(3,6),(4,5)],7) => ([(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
([(0,6),(1,5),(2,4),(3,4),(5,6)],7) => ([(0,6),(1,5),(2,4),(3,4),(5,6)],7) => ([(0,6),(1,5),(2,4),(3,4),(5,6)],7) => ([(0,1),(2,4),(3,4)],5) => 2
([(1,6),(2,6),(3,4),(3,5),(4,5)],7) => ([(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) => 3
([(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) => ([(0,6),(1,6),(2,6),(3,4),(3,5),(4,5)],7) => ([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6) => 3
([(0,3),(1,2),(4,5),(4,6),(5,6)],7) => ([(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) => 3
([(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) => ([(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) => ([(0,6),(1,5),(2,3),(2,4),(3,4),(5,6)],7) => ([(0,5),(1,5),(2,3),(2,4),(3,4)],6) => 3
([(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) => ([(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) => 3
search for individual values
searching the database for the individual values of this statistic
Description
The hat guessing number of a graph.
Suppose that each vertex of a graph corresponds to a player, wearing a hat whose color is arbitrarily chosen from a set of $q$ possible colors. Each player can see the hat colors of his neighbors, but not his own hat color. All of the players are asked to guess their own hat colors simultaneously, according to a predetermined guessing strategy and the hat colors they see, where no communication between them is allowed. The hat guessing number $HG(G)$ of a graph $G$ is the largest integer $q$ such that there exists a guessing strategy guaranteeing at least one correct guess for any hat assignment of $q$ possible colors.
Because it suffices that a single player guesses correctly, the hat guessing number of a graph is the maximum of the hat guessing numbers of its connected components.
Map
connected complement
Description
The componentwise connected complement of a graph.
For a connected graph $G$, this map returns the complement of $G$ if it is connected, otherwise $G$ itself. If $G$ is not connected, the map is applied to each connected component separately.
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 $G$.
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.