AN ALGORITHMIC APPROACH TO EQUITABLE EDGE CHROMATIC NUMBER OF GRAPHS

Year 2019, Volume: 9 Issue: 2, 374 - 383, 01.06.2019

Veninstine Vivik J. Girija G.

Abstract

The equitable edge chromatic number is the minimum number of colors required to color the edges of graph G, for which G has a proper edge coloring and if the number of edges in any two color classes dier by at most one. In this paper, we obtain the equitable edge chromatic number of Sn, Wn, Hn and Gn.

Keywords

Equitable edge coloring, Wheel, Helm, Gear, Sunlet.

References

• [1] J. A. Bondy, U. S. R. Murty, (1976), Graph Theory with Applications, New York; The Macmillan Press Ltd.
• [2] Frank Harary, (1969), Graph Theory, Narosa Publishing home.
• [3] A.J.W.Hilton, D.de Werra, A sufficient condition for equitable edge-colorings of simple graphs, (1994), Discrete Mathematics, V.128, 179-201.
• [4] K. Kaliraj, J. Vernold Vivin, M.M.Ali Akbar, Equitable Coloring on Mycielskian Of Wheels And Bigraphs, (2013), Applied Mathematics E-Notes, V.13, 174-182.
• [5] W. Meyer, Equitable Coloring, (1973), Amer. Math. Monthly, V.80 , 920-922.
• [6] J.Veninstine Vivik and G.Girija, Equitable edge coloring of some graphs, (2015), Utilitas Mathematica, V.96, 27–32.
• [7] V.G. Vizing, Critical graphs with given chromatic class, (1965), Metody Diskret. Analiz, V.5, 9-17.
• [8] Xia Zhang and Guizhen Liu, Equitable edge-colorings of simple graphs, (2010), Journal of Graph Theory, V.66, 175-197.