A006670 Edge-distinguishing chromatic number of path with n nodes.

1, 1, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 12, 12, 12, 12, 12, 12, 12

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn

Comments

This is not the ordinary chromatic number, which is 2 for paths and 2 or 3 for cycles (A006671). - Keith Briggs, Feb 22 2006

The minimum number of colors which can be assigned to the vertices of the path such that each edge e=uv in the path 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

For n > 2, if either r is odd, and r^2 - 2*r + 5 < 2*n <= r^2 + r + 2, or r is even, and r^2 - r + 2 < 2 * n <= r^2 + 2, then a(n) = r [From Al-Wahabi, et al.]. - Sean A. Irvine, Jun 14 2017

Extensions

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