A006671 Edge-distinguishing chromatic number of cycle with n nodes.

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

Author

N. J. A. Sloane

Keywords

• nonn

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

• 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.].

Extensions

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