- FindStat

Identifier

Mp00264: Graphs —delete endpoints⟶ Graphs
St000379: Graphs ⟶ ℤ

Values

([],2) => ([],2) => 0

([],3) => ([],3) => 0

([(1,2)],3) => ([],2) => 0

([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(1,2)],3) => 1

([],4) => ([],4) => 0

([(2,3)],4) => ([],3) => 0

([(1,3),(2,3)],4) => ([],2) => 0

([(0,3),(1,2)],4) => ([],2) => 0

([(1,2),(1,3),(2,3)],4) => ([(1,2),(1,3),(2,3)],4) => 0

([(0,3),(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(1,2)],3) => 1

([(0,2),(0,3),(1,2),(1,3)],4) => ([(0,2),(0,3),(1,2),(1,3)],4) => 1

([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1

([(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) => 3

([],5) => ([],5) => 0

([(3,4)],5) => ([],4) => 0

([(2,4),(3,4)],5) => ([],3) => 0

([(1,4),(2,4),(3,4)],5) => ([],2) => 0

([(1,4),(2,3)],5) => ([],3) => 0

([(1,4),(2,3),(3,4)],5) => ([],2) => 0

([(0,1),(2,4),(3,4)],5) => ([],2) => 0

([(2,3),(2,4),(3,4)],5) => ([(2,3),(2,4),(3,4)],5) => 0

([(1,4),(2,3),(2,4),(3,4)],5) => ([(1,2),(1,3),(2,3)],4) => 0

([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,2)],3) => 1

([(1,3),(1,4),(2,3),(2,4)],5) => ([(1,3),(1,4),(2,3),(2,4)],5) => 0

([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => ([(0,2),(0,3),(1,2),(1,3)],4) => 1

([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 0

([(0,4),(1,3),(2,3),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,2)],3) => 1

([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1

([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 0

([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 0

([(0,1),(2,3),(2,4),(3,4)],5) => ([(1,2),(1,3),(2,3)],4) => 0

([(0,3),(1,2),(1,4),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,2)],3) => 1

([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5) => ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5) => 0

([(0,3),(0,4),(1,2),(1,4),(2,3)],5) => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5) => 1

([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5) => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5) => 1

([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5) => ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5) => 1

([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5) => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1

([(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

([(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) => 3

([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2

([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5) => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5) => 2

([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5) => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5) => 4

([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 6

([(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) => 12

([],6) => ([],6) => 0

([(4,5)],6) => ([],5) => 0

([(3,5),(4,5)],6) => ([],4) => 0

([(2,5),(3,5),(4,5)],6) => ([],3) => 0

([(1,5),(2,5),(3,5),(4,5)],6) => ([],2) => 0

([(2,5),(3,4)],6) => ([],4) => 0

([(2,5),(3,4),(4,5)],6) => ([],3) => 0

([(1,2),(3,5),(4,5)],6) => ([],3) => 0

([(3,4),(3,5),(4,5)],6) => ([(3,4),(3,5),(4,5)],6) => 0

([(1,5),(2,5),(3,4),(4,5)],6) => ([],2) => 0

([(0,1),(2,5),(3,5),(4,5)],6) => ([],2) => 0

([(2,5),(3,4),(3,5),(4,5)],6) => ([(2,3),(2,4),(3,4)],5) => 0

([(1,5),(2,5),(3,4),(3,5),(4,5)],6) => ([(1,2),(1,3),(2,3)],4) => 0

([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => 1

([(2,4),(2,5),(3,4),(3,5)],6) => ([(2,4),(2,5),(3,4),(3,5)],6) => 0

([(0,5),(1,5),(2,4),(3,4)],6) => ([],2) => 0

([(1,5),(2,3),(2,4),(3,5),(4,5)],6) => ([(1,3),(1,4),(2,3),(2,4)],5) => 0

([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0

([(1,5),(2,4),(3,4),(3,5),(4,5)],6) => ([(1,2),(1,3),(2,3)],4) => 0

([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6) => ([(0,2),(0,3),(1,2),(1,3)],4) => 1

([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 0

([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => 1

([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1

([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 0

([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,2),(0,3),(1,2),(1,3)],4) => 1

([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 0

([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0

([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1

([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 0

([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 0

([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0

([(0,5),(1,4),(2,3)],6) => ([],3) => 0

([(1,5),(2,4),(3,4),(3,5)],6) => ([],2) => 0

([(0,1),(2,5),(3,4),(4,5)],6) => ([],2) => 0

([(1,2),(3,4),(3,5),(4,5)],6) => ([(2,3),(2,4),(3,4)],5) => 0

([(1,4),(2,3),(2,5),(3,5),(4,5)],6) => ([(1,2),(1,3),(2,3)],4) => 0

([(0,1),(2,5),(3,4),(3,5),(4,5)],6) => ([(1,2),(1,3),(2,3)],4) => 0

([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => 1

([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => ([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => 0

([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5) => 0

([(1,4),(1,5),(2,3),(2,5),(3,4)],6) => ([(1,4),(1,5),(2,3),(2,5),(3,4)],6) => 0

([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => ([(0,2),(0,3),(1,2),(1,3)],4) => 1

([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6) => ([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6) => 0

([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6) => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5) => 1

([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 0

([(0,5),(1,4),(2,3),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => 1

([(0,5),(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5) => 1

([(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1

([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6) => ([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6) => 0

([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5) => 1

([(0,1),(2,4),(2,5),(3,4),(3,5)],6) => ([(1,3),(1,4),(2,3),(2,4)],5) => 0

([(0,5),(1,5),(2,3),(2,4),(3,4)],6) => ([(1,2),(1,3),(2,3)],4) => 0

([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6) => ([(0,2),(0,3),(1,2),(1,3)],4) => 1

([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5)],6) => ([(0,1),(0,2),(1,2)],3) => 1

([(0,4),(1,2),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => 1

([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 0

([(0,4),(1,4),(2,3),(2,5),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => 1

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search for individual values

searching the database for the individual values of this statistic

Description

The number of Hamiltonian cycles in a graph.
A Hamiltonian cycle in a graph $G$ is a subgraph (this is, a subset of the edges) that is a cycle which contains every vertex of $G$.
Since it is unclear whether the graph on one vertex is Hamiltonian, the statistic is undefined for this 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.