A350292 Triangle read by rows: the n-th row gives the saturated vertex Turán numbers for the cube graph Q_n.

1, 2, 1, 6, 3, 1, 12, 8, 4, 1, 24, 20, 10, 5, 1

Offset

1,2

Comments

The k-th saturated vertex Turán number for the cube graph Q_n is the maximum number of vertices to be deleted from the cube graph such that no subgraph Q_k is complete and each of the deleted vertices being added again completes a subgraph Q_k (see Harborth and Nienborg).

Links

Table of n, a(n) for n=1..15.

Heiko Harborth and Hauke Nienborg, Saturated vertex Turán numbers for cube graphs, Congr. Num. 208 (2011), 183-188.

Mathonline, Cube Graphs

Formula

T(n, n) = 1 and T(n, n-1) = n (see Theorem 2 in Harborth and Nienborg).

Example

n\k |   1    2    3    4    5
----+------------------------
  1 |   1
  2 |   2    1
  3 |   6    3    1
  4 |  12    8    4    1
  5 |  24   20   10    5    1
  ...

Crossrefs

Cf. A350293 (k = 1), A350295 (2nd subdiagonal).

Sequence in context: A356601 A362997 A120108 * A060556 A222969 A132813

Adjacent sequences: A350289 A350290 A350291 * A350293 A350294 A350295

Keyword

nonn,tabl,more

Author

Stefano Spezia, Dec 23 2021

Status

approved