Identifier
Images
([],1) => ([],1) => ([],1) => ([],1)
([],2) => ([],1) => ([],1) => ([],1)
([(0,1)],2) => ([(0,1)],2) => ([],2) => ([],2)
([],3) => ([],1) => ([],1) => ([],1)
([(1,2)],3) => ([(0,1)],2) => ([],2) => ([],2)
([(0,2),(1,2)],3) => ([(0,1)],2) => ([],2) => ([],2)
([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(1,2)],3) => ([],3) => ([],3)
([],4) => ([],1) => ([],1) => ([],1)
([(2,3)],4) => ([(0,1)],2) => ([],2) => ([],2)
([(1,3),(2,3)],4) => ([(0,1)],2) => ([],2) => ([],2)
([(0,3),(1,3),(2,3)],4) => ([(0,1)],2) => ([],2) => ([],2)
([(0,3),(1,2)],4) => ([(0,1)],2) => ([],2) => ([],2)
([(0,3),(1,2),(2,3)],4) => ([(0,1)],2) => ([],2) => ([],2)
([(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(1,2)],3) => ([],3) => ([],3)
([(0,3),(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(1,2)],3) => ([],3) => ([],3)
([(0,2),(0,3),(1,2),(1,3)],4) => ([(0,1)],2) => ([],2) => ([],2)
([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(1,2)],3) => ([],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) => ([],4)
([],5) => ([],1) => ([],1) => ([],1)
([(3,4)],5) => ([(0,1)],2) => ([],2) => ([],2)
([(2,4),(3,4)],5) => ([(0,1)],2) => ([],2) => ([],2)
([(1,4),(2,4),(3,4)],5) => ([(0,1)],2) => ([],2) => ([],2)
([(0,4),(1,4),(2,4),(3,4)],5) => ([(0,1)],2) => ([],2) => ([],2)
([(1,4),(2,3)],5) => ([(0,1)],2) => ([],2) => ([],2)
([(1,4),(2,3),(3,4)],5) => ([(0,1)],2) => ([],2) => ([],2)
([(0,1),(2,4),(3,4)],5) => ([(0,1)],2) => ([],2) => ([],2)
([(2,3),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,2)],3) => ([],3) => ([],3)
([(0,4),(1,4),(2,3),(3,4)],5) => ([(0,1)],2) => ([],2) => ([],2)
([(1,4),(2,3),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,2)],3) => ([],3) => ([],3)
([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,2)],3) => ([],3) => ([],3)
([(1,3),(1,4),(2,3),(2,4)],5) => ([(0,1)],2) => ([],2) => ([],2)
([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => ([(0,1)],2) => ([],2) => ([],2)
([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,2)],3) => ([],3) => ([],3)
([(0,4),(1,3),(2,3),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,2)],3) => ([],3) => ([],3)
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,2)],3) => ([],3) => ([],3)
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => ([(0,1)],2) => ([],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) => ([],3)
([(0,4),(1,3),(2,3),(2,4)],5) => ([(0,1)],2) => ([],2) => ([],2)
([(0,1),(2,3),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,2)],3) => ([],3) => ([],3)
([(0,3),(1,2),(1,4),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,2)],3) => ([],3) => ([],3)
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,2)],3) => ([],3) => ([],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)
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,2)],3) => ([],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) => ([],3)
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,2)],3) => ([],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) => ([],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) => ([],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) => ([],4)
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5) => ([(0,1),(0,2),(1,2)],3) => ([],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) => ([],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) => ([],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) => ([],5)
([],6) => ([],1) => ([],1) => ([],1)
([(4,5)],6) => ([(0,1)],2) => ([],2) => ([],2)
([(3,5),(4,5)],6) => ([(0,1)],2) => ([],2) => ([],2)
([(2,5),(3,5),(4,5)],6) => ([(0,1)],2) => ([],2) => ([],2)
([(1,5),(2,5),(3,5),(4,5)],6) => ([(0,1)],2) => ([],2) => ([],2)
([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => ([(0,1)],2) => ([],2) => ([],2)
([(2,5),(3,4)],6) => ([(0,1)],2) => ([],2) => ([],2)
([(2,5),(3,4),(4,5)],6) => ([(0,1)],2) => ([],2) => ([],2)
([(1,2),(3,5),(4,5)],6) => ([(0,1)],2) => ([],2) => ([],2)
([(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => ([],3) => ([],3)
([(1,5),(2,5),(3,4),(4,5)],6) => ([(0,1)],2) => ([],2) => ([],2)
([(0,1),(2,5),(3,5),(4,5)],6) => ([(0,1)],2) => ([],2) => ([],2)
([(2,5),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => ([],3) => ([],3)
([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => ([(0,1)],2) => ([],2) => ([],2)
([(1,5),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => ([],3) => ([],3)
([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => ([],3) => ([],3)
([(2,4),(2,5),(3,4),(3,5)],6) => ([(0,1)],2) => ([],2) => ([],2)
([(0,5),(1,5),(2,4),(3,4)],6) => ([(0,1)],2) => ([],2) => ([],2)
([(1,5),(2,3),(2,4),(3,5),(4,5)],6) => ([(0,1)],2) => ([],2) => ([],2)
([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => ([(0,1)],2) => ([],2) => ([],2)
([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => ([],3) => ([],3)
([(1,5),(2,4),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => ([],3) => ([],3)
([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => ([(0,1)],2) => ([],2) => ([],2)
([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6) => ([(0,1)],2) => ([],2) => ([],2)
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => ([],3) => ([],3)
([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => ([],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) => ([],3)
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,1)],2) => ([],2) => ([],2)
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,1)],2) => ([],2) => ([],2)
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,1)],2) => ([],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) => ([],3)
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => ([],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) => ([],3)
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,1)],2) => ([],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) => ([],3)
([(0,5),(1,4),(2,3)],6) => ([(0,1)],2) => ([],2) => ([],2)
([(1,5),(2,4),(3,4),(3,5)],6) => ([(0,1)],2) => ([],2) => ([],2)
([(0,1),(2,5),(3,4),(4,5)],6) => ([(0,1)],2) => ([],2) => ([],2)
([(1,2),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => ([],3) => ([],3)
([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => ([(0,1)],2) => ([],2) => ([],2)
([(1,4),(2,3),(2,5),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => ([],3) => ([],3)
([(0,1),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => ([],3) => ([],3)
([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => ([],3) => ([],3)
([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => ([],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) => ([],3)
([(1,4),(1,5),(2,3),(2,5),(3,4)],6) => ([(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)
([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => ([(0,1)],2) => ([],2) => ([],2)
([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => ([],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) => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5) => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
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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
complement
Description
The complement of a graph.
The complement of a graph has the same vertices, but exactly those edges that are not in the original graph.
The complement of a graph has the same vertices, but exactly those edges that are not in the original graph.
Map
delete endpoints
Description
Sends a graph to a maximal subgraph with no endpoints.
An endpoint of a graph is a vertex of degree one. Given an arbitrary graph, this map repeatedly searches for an endpoint and deletes it, until no endpoint remains. The result does not depend on the order of endpoints chosen, up to isomorphism. The map preserves the number of connected components. For a connected graph with at least one cycle, this map returns the 2-core.
An endpoint of a graph is a vertex of degree one. Given an arbitrary graph, this map repeatedly searches for an endpoint and deletes it, until no endpoint remains. The result does not depend on the order of endpoints chosen, up to isomorphism. The map preserves the number of connected components. For a connected graph with at least one cycle, this map returns the 2-core.
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