- FindStat

Identifier

Mp00198: Posets —incomparability graph⟶ Graphs
Mp00274: Graphs —block-cut tree⟶ Graphs
St001060: Graphs ⟶ ℤ

Values

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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search for individual values

searching the database for the individual values of this statistic

Description

The distinguishing index of a graph.
This is the smallest number of colours such that there is a colouring of the edges which is not preserved by any automorphism.
If the graph has a connected component which is a single edge, or at least two isolated vertices, this statistic is undefined.

Map

block-cut tree

Description

Sends a graph to its block-cut tree.
The block-cut tree has a vertex for each block and for each cut-vertex of the given graph, and there is an edge for each pair of block and cut-vertex that belongs to that block. A block is a maximal biconnected (or 2-vertex connected) subgraph. A cut-vertex is a vertex whose removal increases the number of connected components.

Map

incomparability graph

Description

The incomparability graph of a poset.