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.
 

View this paper at   Google Scholar | DPI Digital Library

XML View     PDF Download

How to Cite this Paper

1028 Views    308 Downloads    193 Downloads

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.