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Statistic identifier: St001871

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Collection: Graphs

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Description: The number of triconnected components of a graph.

A connected graph is '''triconnected''' or '''3-vertex connected''' if it cannot be disconnected by removing two or fewer vertices. An arbitrary connected graph can be decomposed as a union of biconnected (2-vertex connected) graphs, known as '''blocks''', and each biconnected graph can be decomposed as a union of components with are either a cycle (type "S"), a cocyle (type "P"), or triconnected (type "R"). The decomposition of a biconnected graph into these components is known as the '''SPQR-tree''' of the graph.

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References: [1]   [[wikipedia:SPQR_tree]]

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Code:


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Statistic values:

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

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Created: Dec 02, 2022 at 00:55 by Harry Richman

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Last Updated: Dec 02, 2022 at 09:23 by Harry Richman