A006670 Edge-distinguishing chromatic number of path with n nodes. (Formerly M0252)

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

1,3

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

Table of n, a(n) for n=1..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

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

Crossrefs

Sequence in context: A366632 A110867 A342010 * A132914 A370461 A060646

Adjacent sequences: A006667 A006668 A006669 * A006671 A006672 A006673

Keyword

nonn

Author

N. J. A. Sloane.

Extensions

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

Status

approved