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Date Published: 28/02/2018
Online Published: 28/02/2018
Abstract Views: 31
Views PDF: 33
DOI: https://doi.org/10.52714/dthu.30.2.2018.556
Issue
No. 30 (2018): Part B - Natural Sciences
Section
Natural Sciences Issue (Vietnamese)
How to Cite
Le, X. H. (2018). Chromatic number, chromatic polynomials and chromatically unique for K2r. Dong Thap University Journal of Science, 30, 90-94. https://doi.org/10.52714/dthu.30.2.2018.556

Chromatic number, chromatic polynomials and chromatically unique for K2r

Xuan Hung Le

Main Article Content

Abstract

One of the fundamental issues in graph theory is the graph-coloring problem. In particular, it is to determine the chromatic number, chromatic polynomials of graphs and to characterize chromatically unique graphs. In this paper, we determine the chromatic number, chromatic polynomials and characterize chromatically unique for K2 r.

Article Details

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

Keywords

Complete r-partite graph, vertex coloring (coloring), chromatic number, chromatic polynomials, chromatically unique graph

References

[1]. M. Behazad and G. Chartrand and J. Cooper (1967), “The coloring numbers of complete Graphs”, J. London Math. Soc., (42), p. 226-228.
[2]. J. C. Bermond (1974), “Nombre chromatique total du graph r-parti complete”, J. London Math. Soc., 9 (2), p. 279-285.
[3]. G. D. Birkhoff (1912), “A determinant formula for the number of ways of coloring a map”, Annals of Math, 14 (2), p. 42-46.
[4]. B. Bollobás (1979), Graph theory: an introductory course, Springer – Verlag. New York, Heidelberg, Berlin.
[5]. D. G. Hoffman and C. A. Roger (1992), “The chromatic index of complete multipartite graphs”, Journal of Graph Theory, (16), p. 159-163.
[6]. Lê Xuân Hùng (2014), “Sắc số, đa thức tô màu và tính duy nhất tô màu của đồ thị tách cực”, Tạp chí Khoa học và Giáo dục, Trường Đại học Sư phạm, Đại học Đà Nẵng, số 13(04), tr. 23-27.
[7]. K. M. Koh and K. L. Teo (1990), “The search for chromatically unique graphs”, Graphs Combin., 6 (3), p. 259-285.
[8]. K. M. Koh and K. L. Teo (1997), “The search for chromatically unique graphs II”, Discrete Math., (172), p. 59-78.
[9]. R. C. Read (1968), “An introduction to chromatic polynomials”, J. Combin. Theory, 4 (1), p. 52-71.
[10]. R. C. Read (1987), “Connectivity and chromatic uniqueness”, Ars Combin., (23), p. 209-218.