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a(n) is the 1st saturated vertex Turán number for the cube graph Q_n.
2

%I #8 Dec 25 2021 14:54:33

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

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

%C 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).

%H Heiko Harborth and Hauke Nienborg, <a href="https://www.researchgate.net/publication/266861957_Saturated_vertex_Turan_numbers_for_cube_graphs">Saturated vertex Turán numbers for cube graphs</a>, Congr. Num. 208 (2011), 183-188.

%H Mathonline, <a href="http://mathonline.wikidot.com/cube-graphs">Cube Graphs</a>

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

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

%Y First column of A350292.

%Y Cf. A000225, A350294.

%K nonn,more

%O 1,2

%A _Stefano Spezia_, Dec 23 2021