BlockCount on LabeledGraph
The blocks: the maximal connected subgraphs with no cut vertex; an isolated vertex is a block.
FindStat's St000553. The blocks of a component are one, plus for each cut vertex the components it leaves, less one; each vertex with an edge adds the components its deletion leaves in its own component, less one. The deleted vertex stays as an isolated one, a component of its own. The graph with no vertices gives 0.
Called as CombinatorialStat(x, "BlockCount"). The head's page has its examples.
Live
Distribution
Over LabeledGraphs at each size, tallied here in your browser; sizes past 6 are not offered.
FindStat St000553
The number of blocks of a graph.
| Object | Value |
|---|---|
([],1) | 1 |
([],2) | 2 |
([],3) | 3 |
([],4) | 4 |
([],5) | 5 |
([],6) | 6 |
([(0,1)],2) | 1 |
([(1,2)],3) | 2 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000553 has the rest.