A338604 Number of unlabeled connected graphs with n edges with degree >= 3 at each node.

1, 0, 1, 3, 5, 9, 27, 67, 198, 646, 2216, 8178, 32095, 132093, 568368, 2541506, 11762657, 56183633, 276288402, 1396172601, 7238931364

Offset

6,4

Links

Table of n, a(n) for n=6..26.

Example

a(10)=5:
There are 5 graphs with 10 edges and degree >=3 at all nodes (see table in A123545):
The complete graph on 5 nodes, given by the edge list
[[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],
and 4 graphs on 6 nodes:
  [[1,3],[1,5],[1,6],[2,4],[2,5],[2,6],[3,5],[3,6],[4,5],[4,6]],
  [[1,4],[1,5],[1,6],[2,4],[2,5],[2,6],[3,4],[3,5],[3,6],[4,6]],
  [[1,3],[1,4],[1,6],[2,4],[2,5],[2,6],[3,5],[3,6],[4,6],[5,6]],
  [[1,3],[1,4],[1,5],[1,6],[2,4],[2,5],[2,6],[3,5],[3,6],[4,6]].
The first one has degree 3 or 4 at all nodes, but becomes disconnected by removing nodes 5 and 6 and their incident edges. It is therefore not 3-connected.
    .--5--.
   /  / \  \
  1--3   4--2
   \  \ /  /
    .--6--.
.
The complete graph on 5 nodes and the last 3 graphs with 6 nodes are all 3-connected. Thus A338511(10)=4, and by inclusion of the graph shown above a(10)=5.

Crossrefs

Cf. A007112, A123545, A338511, A338593, A338594.

Sequence in context: A192152 A217098 A262314 * A209286 A082711 A013622

Adjacent sequences: A338601 A338602 A338603 * A338605 A338606 A338607

Keyword

nonn,hard,more

Author

Hugo Pfoertner, Nov 21 2020

Status

approved