

A006670


Edgedistinguishing 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
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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. AlWahabi, R. Bari, F. Harary and D. Ullman, The edgedistinguishing chromatic number of paths and cycles, pp. 1722 of Graph Theory in Memory of G. A. Dirac (Sandbjerg, 1985). Edited by L. D. Andersen et al., Annals of Discrete Mathematics, 41. NorthHolland Publishing Co., AmsterdamNew 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 AlWahabi, et al.].  Sean A. Irvine, Jun 14 2017


CROSSREFS

Sequence in context: A005707 A087828 A110867 * A132914 A060646 A103298
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



