Equitable total chromatic number of splitting graph
AbstractAmong the varius coloring of graphs, the concept of equitable total coloring of graph G is the coloring of all its vertices and edges in which the number of elements in any two color classes differ by atmost one. The minimum number of colors required is called its equitable total chromatic number. In this paper, we determine an equitable total chromatic number of splitting graph of Pn, Cn and K1,n.
M. Behzad, Graphs and their chromatic numbers, Ph. D. thesis, Michigan State University, East Lansing, MI, USA, 1965.
G. Girija, and J. Veninstine Vivik, “Equitable total coloring of some graphs”, International Journal of Mathematical Combinatorics, vol. 1, pp. 107-112, Mar. 2015. [On line]. Available: https://bit.ly/338wzRo
G. Kun, Z. Zhongfu and W. Jian Fang, “Equitable total coloring of some join graphs”, Journal of mathematical research and exposition, vol. 28, no. 4, pp. 823-828, 2008, doi: 10.3770/j.issn:1000-341X.2008.04.010  H. Wang and J. Wei, “The equitable total chromatic number of the graph HM(Wn)”, Journal of applied mathematics and computing, vol. 24, no. 1-2, pp. 313-323, May 2007, doi: 10.1007/BF02832320.
H. Fu, “Some results on equalized total coloring”, Congressus numerantium, vol. 102, pp. 111-119, 1994.
M. Gang and M. Ming, “The equitable total chromatic number of the some join-graphs”, Open journal of applied sciences, vol. 2 no. 4B, pp. 96-99, Jan. 2012, doi: 10.4236/ojapps.2012.24B023.
M. Gang, Z. Zhong-fu, “On the equitable total coloring of multiple join graph”, Journal of mathematical research and exposition, no. 2, pp. 351-354, 2007. [On line]. Available: https://bit.ly/2q0KcE5
E. Sampathkumar and H. Walikar, “On spliting graph of a graph”, Journal of the Karnatak University-Science, vol. 25-26, pp. 13-16, 1980-1981. [On line]. Available: https://bit.ly/2LYpb5a
T. Chunling, L. Xiaohui, Y. Yuansheng and L. Lizhihe, “Equitable total coloring of Cm2 Cn”, Discrete applied mathematics, vol. 157, no. 4, pp. 596-601, Feb. 2009, doi: 10.1016/j.dam.2008.08.030.
V. Vivik J. y G. Girija, “An algorithmic approach to equitable total chromatic number of graphs”, Proyecciones (Antofagasta, En línea), vol. 36, no. 2, pp. 307-324, Jun. 2017, doi: 10.4067/S0716-09172017000200307
V. Vizing, “On an estimate of the chromatic class of a p− graph”, (in Russian), Diskret. Analiz., no. 5, pp. 25-30, 1964.
W. Wang, “Equitable Total Coloring of Graphs with Maximum Degree 3”, Graphs and combinatorics, vol. 18, no. 3, pp. 677–685, Oct. 2002, doi: 10.1007/s003730200051.
Z. Zhang, W. Wang, S. Bau and J. Li, “On the equitable total coloring of some join graphs”, Journal of information and computational science, vol. 2, no. 4, pp. 829-834, 2005.
Z. Zhang, J. Zhang, J. Wang, “The total chromatic number of some graph”, Scientia Sinica. Series A. 31, 12, pp. 1434-1441, (1988).
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