Vertex Colorings of Graph and Some of Their Applications in Promoting Global Competitiveness for National Growth and Productivity
Machine Learning Research
Volume 3, Issue 2, June 2018, Pages: 28-32
Received: Jul. 28, 2018;
Accepted: Aug. 21, 2018;
Published: Sep. 19, 2018
Views 512 Downloads 14
Abdulazeez Idris, Department of Mathematics, Ahmadu Bello University, Zaria, Nigeria
Bashir Ismail, Department of Mathematics, Ahmadu Bello University, Zaria, Nigeria
Mustapha Usman Jama’are, Department of Mathematics, Ahmadu Bello University, Zaria, Nigeria
Dahiru Zaharaddeen, Department of Mathematics, Federal University, Dutsinma, Nigeria
Follow on us
This paper studies various results on vertex colorings of simple connected graphs, chromatic number, chromatic polynomials and some Algebraic properties of chromatic polynomials. Results were obtained on the roots of chromatic polynomials of simple connected graphs based on Read’s conjecture. The chromatic number of every graph is the minimum number of colors to properly color the graph. Chromatic polynomial of a graph is a polynomial in integer and the leading coefficient of chromatic polynomial of a graph of order n and size m is always 1, whose coefficient alternate in sign. Through the application of famous graph theorem (the hand shaking lemma) by whiskey which states that: “the order of a graph twice its size”. Hence, every graph has a chromatic polynomial but not all polynomials are chromatic. For example, the polynomial λ5 − 11 λ4 + 14 λ3 − 6 λ2 + 2 λ is a polynomial for a graph on five vertices and eleven edges which does not exists. Because the maximum number size for a graph of order five is ten. The paper equally gave some practical applications of Vertex coloring in real life situations such as scheduling, allocation of channels to television and radio stations, separation of chemicals and traffic light signals.
Adjacent Vertices, Chromatic Number, Chromatic Polynomials
To cite this article
Mustapha Usman Jama’are,
Vertex Colorings of Graph and Some of Their Applications in Promoting Global Competitiveness for National Growth and Productivity, Machine Learning Research.
Vol. 3, No. 2,
2018, pp. 28-32.
Copyright © 2018 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/
) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Bondy J. A. (1976). Graphs theory with applications, the MACMILAN PRESS LTD London, pp. 131-133.
David G. (2013). An introduction to combinatorics and graph theory, California, USA: Creative Commons publisher, Pp. 85 -86.
Gary C. (2009). Chromatic graph theory, U.S.A: Taylor & Francis Group, Pp. 14-167.
Kalamazoo R. (2003). Graph theory, Yugoslau journal of Operations Research, vol. 13, pp. 208-210.
Srinivas B. R. (2014). Chromatic polynomials, International Journal of Scientific and Innovative Mathematical Research IJSIMR) Volume 2, Issue 11, November, PP 918-920.
Tamas H. (2009). the chromatic polynomials, (journal) EOTVOS LO RAND University, vol 12, pp. 12-18.
Thuslasiraman K. (1992). Graphs; theory and algorithm, New York: John Wiley and sons, Inc. 1992, pp. 253- 254.
Oystein O. (1962). Theory of graphs, USA: American mathematical society, pp. 2-22.
Sabyasach M. eta’l (2013). Application of Vertex coloring in a particular triangular closed path structure and in Kraft’s inequality. American Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS). Vol. 1. Arxiv.org/pdf/1309.3513.pdf.
Ridhi J. Eta’l (2016). Graph coloring and its implementation, international Journal of Advance Research and Innovation in technology. (vol. 2, issue 5).