Published 2018-07-01
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.
References
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[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[6] P. Pandey and J. V. Kureethara, “L(t, 1)-colouring of graphs,” unpublished.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.
[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[6] P. Pandey and J. V. Kureethara, “L(t, 1)-colouring of graphs,” unpublished.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.