SOME RESULTS ON TOTAL CHROMATIC NUMBER OF A GRAPH

Year 2017, Volume: 7 Issue: 2, 332 - 336, 01.12.2017

S. K. Vaidya Rakhimol V. Isaac

Abstract

A total coloring of a graph is a proper coloring in which no two adjacent or incident graph elements receive the same color. The total chromatic number of a graph is the smallest positive integer for which the graph admits a total coloring. In this paper, we derive some results on total chromatic number of a graph.

Keywords

total coloring , total chromatic number , splitting graph.

References

• Behzad,M., (1965), Graphs and their chromatic numbers, Ph.D Thesis, Michigan University.
• Behzad,M., Chartrand,G., and Cooper,Jr.J.K., (1967), The colour numbers of complete graphs, J. London Math. Soc., 42, pp.226-228.
• Irving,R.W. and Manlove,D.F., (1999), The b-chromatic number of a graph, Discrete Applied Math- ematics, 91,(1-3), pp.127-141.
• Kostochka,A.V., (1996), The total chromatic number of any multigraph with maximum degree five is at most seven, Discrete Math, 162, pp.199-214.
• Rosenfeld,M., (1971), On the total coloring of certain graphs, Israel J. Math., 9(3), pp.396-402.
• Vaidya,S.K. and Barasara,C.M., (2011), Product Cordial Graphs in the Context of Some Graph Operations, International Journal of Mathematics and Scientific Computing, 1(3), pp.1-6.
• Vaidya,S.K., Dani,N.A., Kanani,K.K., and Vihol,P.L., (2011), Cordial and 3-equitable Labeling for Some Wheel Related Graphs, IAENG International Journal of Applied Mathematics , 41(2), pp.99- 105.
• Vaidya,S.K. and Isaac,Rakhimol V., (2015), Total coloring of some cycle related graphs, IOSR Journal of Mathematics, 11(3)(V), pp.51-53.
• Vijayaditya,N., (1971), On total chromatic number of a graph, J. London Math Soc., 2(3), pp.405-408.
• Vizing,V.G., (1968), Some unsolved problems in graph theory, Uspekhi Mat. Nauk (in Russian), 23(6)
• pp.117-134 and in Russian Mathematical Surveys, 23(6), pp.125-141.
• Yap,H.P., (1996), Total colourings of graphs,in: Lecture Notes in Mathematics, 1623, pp.6.
• S. K. Vaidya for the photography and short autobiography, see TWMS J. App. Eng. Math., V.4, N.1, 2014.