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L(t, 1)-Colouring of Wheel Graphs

P. Pandey1 , J. V. Kureethara2

1 Dept. of Mathematics and Statistics, Christ University, Bengaluru, India.
2 Dept. of Mathematics and Statistics, Christ University, Bengaluru, India.

Correspondence should be addressed to: frjoseph@christuniversity.in.


Section:Research Paper, Product Type: Isroset-Journal
Vol.4 , Issue.6 , pp.23-25, Dec-2017


CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v4i6.2325


Online published on Dec 31, 2017


Copyright © P. Pandey, J. V. Kureethara . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
 

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Citation :
IEEE Style Citation: P. Pandey, J. V. Kureethara, “L(t, 1)-Colouring of Wheel Graphs”, International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.4, Issue.6, pp.23-25, 2017.

MLA Style Citation: P. Pandey, J. V. Kureethara "L(t, 1)-Colouring of Wheel Graphs." International Journal of Scientific Research in Mathematical and Statistical Sciences 4.6 (2017): 23-25.

APA Style Citation: P. Pandey, J. V. Kureethara, (2017). L(t, 1)-Colouring of Wheel Graphs. International Journal of Scientific Research in Mathematical and Statistical Sciences, 4(6), 23-25.

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Abstract :
An L(t, 1)-Colouring of graph is the colouring of the vertices of a graph with non negative integers such that the vertices which are adjacent to each other receives colour with their colour difference not belonging to set T with integers including 0 and the vertices which are at distance 2 gets distinct colours. This is a type of channel assignment problem. Allotting frequencies to the radio channels in a region is determined by non-overlapping nature of the transmissions. The L(t, 1)-Colouring takes the inspiration from the famous T-Colouring and L(h, k)-Colouring of graphs. Both are celebrated colouring schemes. The L(t, 1)-span of the graph 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 wheel graphs with respect a set T with consecutive integers and a set T whose elements are in AP with common difference d.

Key-Words / Index Term :
L(t, 1)-colouring, Communication networks, Channel assignment, Radio frequency, Colour span, Wheel Graphs

References :
[1] B. H. Metzger, “Spectrum management technique,” in 38th National ORSA meeting, Detroit, MI, US, 1970.
[2] W. K. Hale, “Frequency assignment: Theory and applications,” in “Proc. IEEE”, Vol. 68, pp. 1497-1514, 1980.
[3] F. S. Roberts, “T-colorings of graphs: recent results and open problems,” “Discrete Mathematics”, Vol. 93, pp. 229-245, 1991.
[4] R. K. Yeh, “Labelling graphs with a condition at distance two,” Ph. D. Thesis, University of South Carolina, 1990.
[5] P. Pandey, J. V. Kureethara, “L(t, 1)-colouring of graphs,” arXiv:1711.03096.
[6] D. B. West, “Introduction to Graph Theory”, 2nd ed. Prentice Hall, US, 2001.
[7] F. Harary, “Graph Theory”, Addison-Wesley, US, 1969.
[8] S. Zhang and Q. Ma, “Labelling of some planar graphs with a condition at distance two,” Journal of Applied Mathematics and Computing, Vol. 24, pp. 421-426, 2007.
[9] P. Pandey, J. V. Kureethara, “L(t, 1)-colouring of cycles”, in ICCTCEEC, Mysore, India, pp. 185-190, 2017.

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