Equitable edge chromatic number of P_{m}⊗S_{n}⁰ and S_{m}⁰⊗S_{n}⁰

Year 2019, Volume: 68 Issue: 2, 1294 - 1300, 01.08.2019

J. Veninstine Vivik

https://doi.org/10.31801/cfsuasmas.524481

Abstract

The equitable edge chromatic number is the minimum number of colors required to color the edges of a graph G and satisfies the criterion, if for each vertex v∈V(G), the number of edges of any one color incident with v differs from the number of edges of any other color incident with v by atmost one. In this paper, the equitable edge chromatic number of tensor product of Path P_{m} coupled with Crown S_{n}⁰ and also two Crown graphs S_{m}⁰ along with S_{n}⁰ are obtained.

Keywords

Equitable edge coloring, tensor product, Crown graph

References

• Bondy, J. A. and Murty, U. S. R., Graph Theory with Applications, New York; The Macmillan Press Ltd, 1976.
• Harary, Frank, Graph Theory, Narosa Publishing home 1969.
• Hilton, A.J.W. and de Werra, D.,A sufficient condition for equitable edge-colorings of simple graphs, Discrete Mathematics 128, (1994), 179-201.
• Meyer, W., Equitable Coloring, Amer. Math. Monthly, 80 (1973), 920-922.
• Veninstine Vivik, J. and Girija, G., Equitable edge coloring of some graphs, Utilitas Mathematica, 96, (2015), 27--32.
• Veninstine Vivik, J., and Girija, G., Equitable Edge Chromatic Number of Mycielskian of Graphs, Far East Journal of Mathematics, 101(9), 2017, 1887-1895.
• Vizing, V.G., Critical graphs with given chromatic class, Metody Diskret. Analiz., 5(1965), 9-17.
• Weichsel, Paul.M., The Kronecker product of graphs, Proc. Amer. Math. Society, Vol.8, (1962), 47-52.
• Lin, Wu-Hsiung and Chang, Gerard, J., Equitable Colorings of Kronecker product of Graphs, Discrete Applied Mathematics, Vol.158, (2010), 1816-1826.
• Zhang, Xia and Liu, Guizhen, Equitable edge-colorings of simple graphs, Journal of Graph Theory, 66, (2010), 175-197.