A339205 Number of 2-connected multigraphs with n edges rooted at two noninterchangeable vertices and have no decomposition into parallel components rooted at the two distinguished vertices.

1, 0, 0, 0, 1, 6, 39, 221, 1237

Offset

1,6

Comments

Variant of A339123, treating the distinguished points as not interchangeable.

Graphs that are 2-connected also have no decomposition into series components, so the graphs enumerated by this sequence are the minimal subset of oriented networks which when combined in series and parallel produce all possible networks with a source and a sink and in which every edge lies on a path between the source and the sink.

Links

Table of n, a(n) for n=1..9.

Example

a(6) = 6, Figures 5 and 6 are A/Z-mirrored images of 1 and 3:
.
      A          A          A          A          A          A
    // \        / \        d \        / \        / \        / \
   //   \      /___\      /   \      /   \      /   \      /   \
   o-----o    o --- o    o-----o    o--o--o    o-----o    o-----o
    \   /      \   /      \   /      \   /     \\   /      \   /
     \ /        \ /        \ /        \ /       \\ /        q /
      Z          Z          Z          Z          Z          Z
.
    Fig. 1     Fig. 2     Fig. 3     Fig. 4     Fig. 5    Fig. 6

Crossrefs

Cf. A338999, A339045, A339123.

Sequence in context: A007793 A297579 A229600 * A258342 A037592 A037683

Adjacent sequences: A339202 A339203 A339204 * A339206 A339207 A339208

Keyword

nonn,more

Author

Rainer Rosenthal, Nov 27 2020

Status

approved