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 A006670 Edge-distinguishing chromatic number of path with n nodes. (Formerly M0252) 0
 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 (list; graph; refs; listen; history; text; internal format)
 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 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: A087828 A330779 A110867 * A132914 A060646 A103298 Adjacent sequences:  A006667 A006668 A006669 * A006671 A006672 A006673 KEYWORD nonn AUTHOR EXTENSIONS More terms and title improved by Sean A. Irvine, Jun 14 2017 STATUS approved

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Last modified August 4 01:48 EDT 2020. Contains 336201 sequences. (Running on oeis4.)