Relation between Center Coloring and the other Colorings

Year 2018, Volume: 3 Issue: 1, 28 - 37, 04.01.2018

Zeynep Ors Yorgancioglu Pinar Dundar Mehmet Umit Gursoy

https://doi.org/10.28978/nesciences.379317

Abstract

In this paper, center coloring and center coloring number are defined, some bounds are established for the center coloring number of a graph in terms of other graphical coloring parameters, and a polynomial time algorithm is proposed in order to calculate the center coloring of a graph.

Keywords

Graph Coloring, center coloring, center coloring number

References

• Aldous, J. M. & Wilson, R. J. (2006). Graphs and Applications, Springer, Great Britain.
• Buckley, F. & Harary, F. (1990). Distance in Graphs, Addision-Wesley Publishing Comp., California USA.
• Chartrand, G. & Lesniak, L. (2005). Graphs & Digraphs, Chapman & Hall/CRC Press, USA.
• Chartrand, G., Okamoto F., Rasmussen C. W. & Zhang P. (2009). The Set Chromatic Number of a Graph, Discussiones Mathematicae Graph Theory, 29, 545-561.
• Immelman, Y. (2007). On The (Upper) Line-Distinguishing and (Upper) Harmonious Chromatic Numbers of a Graph, Dissertation, University of Johannesburg Faculty of Science.
• Kubale, M. (2004). Contemporary Mathematics 352 Graph Colorings, American Mathematical Society, USA. Li, X. & Sun, Y. (2012). Rainbow Connections of Graphs, Springer, London.
• Miller, Z. & Pritikin, D. (1991). The Harmonious coloring number of a graph, Discrete Mathematics, 93, 211-228.
• Vernold, V. J. & Akbar, A. M. M. (2009). On Harmonious Coloring of Middle Graph of and , Note di Matematica, 29, 201-211.
• Yorgancioglu, Z. & Dundar, P. (2011). Total Coloring of Double Vertex Graphs, M.Sc., Ege University, Institute of Science and Technology, 34.
• Yorgancıoğlu, Z. O., Dundar, P. & Berberler, M. E. (2015). The Center Coloring of a graph, Journal of Discrete Mathematical Sciences & Cryptography, 18, 531-540.