A376313 Independence number of the 2-supertoken graph FF_2(C_n) of the cycle C_n on n vertices.

2, 3, 6, 7, 12, 14, 20, 22, 30, 33, 42, 45, 56, 60, 72, 76, 90, 95, 110, 115, 132, 138, 156, 162, 182, 189, 210, 217, 240, 248, 272, 280, 306, 315, 342, 351, 380, 390, 420, 430, 462, 473, 506, 517, 552, 564, 600, 612, 650, 663, 702, 715, 756, 770, 812, 826, 870, 885, 930, 945, 992, 1008

Offset: 2

Author

Miquel A. Fiol, Sep 26 2024

Keywords

• nonn
• easy

Comments

Given a graph G on n vertices and an integer k>=1, the k-supertoken (or reduced k-th power) FF_k(G) of G has vertices representing configurations of k indistinguishable tokens in the (not necessarily different) vertices of G, with two configurations being adjacent if one can be obtained from the other by moving one token along an edge of G.

Links

• R. H. Hammack and G. D. Smith, Cycle bases of reduced powers of graphs, Ars Math. Contemp. 12 (2017) 183-203.

Formula

a(n) = k*(n+2) if n=4*k or n=4*k+1, and a(n)=(k+1)*n if n=4*k+2 or n=4*k+3.