L(t, 1)-Colouring of Cycles

  • Priyanka Pandey CHRIST (Deemed to be University)
  • Joseph Varghese Kureethara CHRIST (Deemed to be University)

Abstract

For a given finite set T including zero, an L(t, 1)-colouring of a graph G is an assignment of non-negative integers to the vertices of G such that the difference between the colours of adjacent vertices must not belong to the set T and the colours of vertices that are at distance two must be distinct. For a graph G, the L(t, 1)-span of G  is the minimum of the highest colour used to colour the vertices of a graph out of all the possible L(t, 1)-colourings. We study the L(t, 1)-span of cycles with respect to specific sets.

Author Biographies

Priyanka Pandey, CHRIST (Deemed to be University)

Research Scholar, CHRIST (Deemed to be University)

Joseph Varghese Kureethara, CHRIST (Deemed to be University)

CHRIST (Deemed to be University)

References

[1] G. Chartrand and P. Zhang, Chromatic Graph Theory, CRC Press, 2009.
[2] J. Georges and D. Mauro, “Generalized vertex labelings with a condition at distance two,” Congr. Numer. vol. 109, pp. 141-159, 1995.
[3] W. K. Hale, “Frequency assignment: Theory and applications,” Proc. IEEE, vol. 68, pp. 1497-1514, 1980.
[4] B. H. Metzger, “Spectrum Management Technique”, presented at 38th National ORSA meeting, Detroit, MI, 1970.
[5] P. Pandey and J. V. Kureethara, “L(t, 1)-colouring of cycles,” Proc. ICCTCEEC, vol. 1, pp. 185-190, Sep. 2017.
[6] P. Pandey and J. V. Kureethara, “L(t, 1)-colouring of graphs,” unpublished.
[7] P. Pandey and J. V. Kureethara, “L(t, 1)-colouring of wheel graphs,” Int. J. Scientific Res. Math. Stat. Sci. vol. 4, no. 6, pp. 23-25, 2017.
Published
2018-07-01
Section
Research Articles