A208648 - OEIS

A208648

Denominators of Pokrovskiy's lower bound on the ratio of e(G^n) the number of edges in the n-th power of a graph G, to E(G) the number of edges of G.

2, 1, 1, 4, 1, 1, 6, 1, 1, 8, 1, 1, 10, 1, 1, 12

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OFFSET

0,1

COMMENTS

Numerators are A208647. The fractions begin: 1/2, 1/2, 7/4, 2/1, 2/1, 17/6, 3/1, 3/1, 31/8, 4/1, 4/1, 49/10, 5/1, 5/1, 71/12.

LINKS

Alexey Pokrovskiy, Edge growth in graph powers, arXiv:1202.6085v1 [math.CO], Feb 27, 2012.

FORMULA

If n == 0 (mod 3) then e(G^n)/e(G) = ((n+3)/3) - 3/(2*(n+3));

If n =/= 0 (mod 3) then e(G^n)/e(G) = ceiling(n/3).

CROSSREFS

Cf. A003417 (continued fraction for e), A208647.

KEYWORD

nonn,easy,frac

AUTHOR

STATUS

approved