List-Chromatic Number and Chromatically Unique of the Graph Kr2 + Ok
DOI:
https://doi.org/10.17268/sel.mat.2019.01.04Keywords:
Chromatic number, list-chromatic number, chromatic polinomial, chromatically unique graph, complete r-partite graphAbstract
In this paper, we determine list-chromatic number and characterize chromatically unique of the graph G = Kr2 +Ok. We shall prove that ch(G) = r + 1 if 1<=k<=2, G is x-unique if 1<=k<=3.
References
Behzad, M. Graphs and thei chromatic number, Doctoral Thesis (Michigan State University), 1965.
Behzad, M. and Chartrand, G. Introduction to the theory of graphs, Allyn and Bacon, Boston 1971.
Behzad, M., Chartrand G. and Cooper,J. The coloring numbers of complete graphs, J. London Math. Soc. 42 (1967), 226 – 228.
Birkhoff, G. D. A determinant formula for the number of ways of coloring a map, Annals of Math. 14 (2) (1912) 42–46.
Bondy, J.A. and Murty, U.S.R. Graph theory with applications, MacMillan, 1976.
Brandstadt, A., Hammer, P.L., Le, V.B. and Lozin, V.V. Bisplit graphs, Discrete Math. 299 (2005) 11–32.
Chao, C.Y., Whitehead, Jr. E.G. On chromatic equivalence of graphs. In: Theory and Applications of Graphs, ed. Y. Alavi and D.R. Lick, Springer Lecture Notes in Math. 642 (1978) 121–131.
Chvatal, V. and Hammer, P.L. Aggregation of inequalities in integer programming, Annals Disc. Math. 1 (1977) 145–162.
Diestel, R. Graph Theory, Springer – Verlag New Your 2000.
Koh, K.M. and Teo, K.L. The search for chromatically unique graphs, Graphs Combin. 6 (1990) 259–285.
Koh, K.M. and Teo, K.L. The search for chromatically unique graphs II, Discrete Math. 172 (1997) 59–78.
Read,R.C. An introduction to chromatic polynomials, J. Combin. Theory 4 (1968) 52–71.
Ngo Dac Tan and Le Xuan Hung. On colorings of split graphs, Acta Mathematica Vietnammica, Volume 31, Number 3, 2006, pp. 195– 204.
Vizing, V.G. On an estimate of the chromatic class of a p-graph, Discret. Analiz. 3 (1964) 23–30. (In Russian)
Wilson, R.J. Introduction to graph theory, Longman group ltd, London (1975).
Published
How to Cite
Issue
Section
License
The authors who publish in this journal accept the following conditions:
1. The authors retain the copyright and assign to the journal the right of the first publication, with the work registered with the Creative Commons Attribution License,Atribución 4.0 Internacional (CC BY 4.0) which allows third parties to use what is published whenever they mention the authorship of the work And to the first publication in this magazine.
2. Authors may make other independent and additional contractual arrangements for non-exclusive distribution of the version of the article published in this journal (eg, include it in an institutional repository or publish it in a book) provided they clearly state that The paper was first published in this journal.
3. Authors are encouraged to publish their work on the Internet (for example, on institutional or personal pages) before and during the review and publication process, as it can lead to productive exchanges and to a greater and more rapid dissemination Of the published work.