A006671 Edge-distinguishing chromatic number of cycle with n nodes. (Formerly M2269)

3, 3, 3, 3, 4, 4, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 12, 12, 12, 12, 12, 12, 13, 13

Offset

3,1

Comments

The minimum number of colors which can be assigned to the vertices of the cycle such that each edge e=uv in the cycle is assigned a different "color" {c(u),c(v)}. - Sean A. Irvine, Jun 14 2017

References

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Table of n, a(n) for n=3..74.

K. Al-Wahabi, R. Bari, F. Harary and D. Ullman, The edge-distinguishing chromatic number of paths and cycles, pp. 17-22 of Graph Theory in Memory of G. A. Dirac (Sandbjerg, 1985). Edited by L. D. Andersen et al., Annals of Discrete Mathematics, 41. North-Holland Publishing Co., Amsterdam-New York, 1989.

Formula

If either r is odd, and r^2 - 2*r + 1 < 2*n <= r^2 + r, or r is even, and r^2 - r < 2 * n <= r^2, then a(n) = r [From Al-Wahabi, et al.].

Crossrefs

Sequence in context: A262994 A179847 A035936 * A046074 A328914 A295084

Adjacent sequences: A006668 A006669 A006670 * A006672 A006673 A006674

Keyword

nonn

Author

N. J. A. Sloane.

Extensions

More terms and title improved by Sean A. Irvine, Jun 14 2017

Status

approved