Identifier
Mp00154:
Graphs
—core⟶
Graphs
Mp00037: Graphs —to partition of connected components⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
Mp00037: Graphs —to partition of connected components⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
Images
([],1) => ([],1) => [1] => []
([],2) => ([],1) => [1] => []
([(0,1)],2) => ([(0,1)],2) => [2] => []
([],3) => ([],1) => [1] => []
([(1,2)],3) => ([(0,1)],2) => [2] => []
([(0,2),(1,2)],3) => ([(0,1)],2) => [2] => []
([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(1,2)],3) => [3] => []
([],4) => ([],1) => [1] => []
([(2,3)],4) => ([(0,1)],2) => [2] => []
([(1,3),(2,3)],4) => ([(0,1)],2) => [2] => []
([(0,3),(1,3),(2,3)],4) => ([(0,1)],2) => [2] => []
([(0,3),(1,2)],4) => ([(0,1)],2) => [2] => []
([(0,3),(1,2),(2,3)],4) => ([(0,1)],2) => [2] => []
([(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(1,2)],3) => [3] => []
([(0,3),(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(1,2)],3) => [3] => []
([(0,2),(0,3),(1,2),(1,3)],4) => ([(0,1)],2) => [2] => []
([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(1,2)],3) => [3] => []
([(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) => [4] => []
([],5) => ([],1) => [1] => []
([(3,4)],5) => ([(0,1)],2) => [2] => []
([(2,4),(3,4)],5) => ([(0,1)],2) => [2] => []
([(1,4),(2,4),(3,4)],5) => ([(0,1)],2) => [2] => []
([(0,4),(1,4),(2,4),(3,4)],5) => ([(0,1)],2) => [2] => []
([(1,4),(2,3)],5) => ([(0,1)],2) => [2] => []
([(1,4),(2,3),(3,4)],5) => ([(0,1)],2) => [2] => []
([(0,1),(2,4),(3,4)],5) => ([(0,1)],2) => [2] => []
([(2,3),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,2)],3) => [3] => []
([(0,4),(1,4),(2,3),(3,4)],5) => ([(0,1)],2) => [2] => []
([(1,4),(2,3),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,2)],3) => [3] => []
([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,2)],3) => [3] => []
([(1,3),(1,4),(2,3),(2,4)],5) => ([(0,1)],2) => [2] => []
([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => ([(0,1)],2) => [2] => []
([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,2)],3) => [3] => []
([(0,4),(1,3),(2,3),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,2)],3) => [3] => []
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,2)],3) => [3] => []
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => ([(0,1)],2) => [2] => []
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,2)],3) => [3] => []
([(0,4),(1,3),(2,3),(2,4)],5) => ([(0,1)],2) => [2] => []
([(0,1),(2,3),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,2)],3) => [3] => []
([(0,3),(1,2),(1,4),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,2)],3) => [3] => []
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,2)],3) => [3] => []
([(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),(0,4),(1,3),(2,3),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,2)],3) => [3] => []
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,2)],3) => [3] => []
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,2)],3) => [3] => []
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => [4] => []
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => [4] => []
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => [4] => []
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5) => ([(0,1),(0,2),(1,2)],3) => [3] => []
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,2)],3) => [3] => []
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => [4] => []
([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => [5] => []
([],6) => ([],1) => [1] => []
([(4,5)],6) => ([(0,1)],2) => [2] => []
([(3,5),(4,5)],6) => ([(0,1)],2) => [2] => []
([(2,5),(3,5),(4,5)],6) => ([(0,1)],2) => [2] => []
([(1,5),(2,5),(3,5),(4,5)],6) => ([(0,1)],2) => [2] => []
([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => ([(0,1)],2) => [2] => []
([(2,5),(3,4)],6) => ([(0,1)],2) => [2] => []
([(2,5),(3,4),(4,5)],6) => ([(0,1)],2) => [2] => []
([(1,2),(3,5),(4,5)],6) => ([(0,1)],2) => [2] => []
([(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => [3] => []
([(1,5),(2,5),(3,4),(4,5)],6) => ([(0,1)],2) => [2] => []
([(0,1),(2,5),(3,5),(4,5)],6) => ([(0,1)],2) => [2] => []
([(2,5),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => [3] => []
([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => ([(0,1)],2) => [2] => []
([(1,5),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => [3] => []
([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => [3] => []
([(2,4),(2,5),(3,4),(3,5)],6) => ([(0,1)],2) => [2] => []
([(0,5),(1,5),(2,4),(3,4)],6) => ([(0,1)],2) => [2] => []
([(1,5),(2,3),(2,4),(3,5),(4,5)],6) => ([(0,1)],2) => [2] => []
([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => ([(0,1)],2) => [2] => []
([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => [3] => []
([(1,5),(2,4),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => [3] => []
([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => ([(0,1)],2) => [2] => []
([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6) => ([(0,1)],2) => [2] => []
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => [3] => []
([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => [3] => []
([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => [3] => []
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,1)],2) => [2] => []
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,1)],2) => [2] => []
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,1)],2) => [2] => []
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => [3] => []
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => [3] => []
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => [3] => []
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,1)],2) => [2] => []
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => [3] => []
([(0,5),(1,4),(2,3)],6) => ([(0,1)],2) => [2] => []
([(1,5),(2,4),(3,4),(3,5)],6) => ([(0,1)],2) => [2] => []
([(0,1),(2,5),(3,4),(4,5)],6) => ([(0,1)],2) => [2] => []
([(1,2),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => [3] => []
([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => ([(0,1)],2) => [2] => []
([(1,4),(2,3),(2,5),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => [3] => []
([(0,1),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => [3] => []
([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => [3] => []
([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => [3] => []
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => [3] => []
([(1,4),(1,5),(2,3),(2,5),(3,4)],6) => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5) => [5] => []
([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => ([(0,1)],2) => [2] => []
([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => [3] => []
([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6) => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5) => [5] => []
>>> Load all 208 entries. <<<Map
core
Description
The core of a graph.
The core of a graph $G$ is the smallest graph $C$ such that there is a homomorphism from $G$ to $C$ and a homomorphism from $C$ to $G$.
Note that the core of a graph is not necessarily connected, see [2].
The core of a graph $G$ is the smallest graph $C$ such that there is a homomorphism from $G$ to $C$ and a homomorphism from $C$ to $G$.
Note that the core of a graph is not necessarily connected, see [2].
Map
to partition of connected components
Description
Return the partition of the sizes of the connected components of the graph.
Map
first row removal
Description
Removes the first entry of an integer partition
searching the database
Sorry, this map was not found in the database.