A350293 a(n) is the 1st saturated vertex Turán number for the cube graph Q_n.

1, 2, 6, 12, 24, 52, 112

Offset: 1

Author

Stefano Spezia, Dec 23 2021

Keywords

• nonn
• more

Comments

The 1st 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_1 is complete and each of the deleted vertices being added again completes a subgraph Q_1 (see Harborth and Nienborg).

Links

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

Crossrefs

First column of A350292.

Cf. A000225, A350294.

Formula

a(n) = n*2^n/(n + 1) iff n is a Mersenne number (see Theorem 1 in Harborth and Nienborg).

a(n) <= A350294(n) (see Lemma 1 in Harborth and Nienborg).