Cyclically Interval Total Coloring of the One Point Union of Cycles
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Abstract: A total coloring of a graph G with colors 1, 2, ..., t is called a cyclically interval total t-coloring if all colors are used, and the edges incident to each vertex v∈V(G) together with v are colored by (dG(v)+1) consecutive colors modulo t, where dG(v) is the degree of the vertex v in G. The one point union 
of k-copies of cycle Cn is the graph obtained by taking v as a common vertex such that any two distinct cycles 
and 
are edge disjoint and do not have any vertex in common except v. In this paper, we study the cyclically interval total colorings of 
, where n≥3 and k≥2.
of k-copies of cycle Cn is the graph obtained by taking v as a common vertex such that any two distinct cycles and are edge disjoint and do not have any vertex in common except v. In this paper, we study the cyclically interval total colorings of , where n≥3 and k≥2.Keywords:
Total Coloring,
Interval Total Coloring,
Cyclically Interval Total Coloring,
Cycle,
One Point Union of Cycles
Cite this paper:
Su, S. , Zhao, W. and Zhao, Y. (2018) Cyclically Interval Total Coloring of the One Point Union of Cycles. Open Journal of Discrete Mathematics, 8, 65-72. doi: 10.4236/ojdm.2018.83006.
References
[1] Vizing, V.G. (1965) Chromatic Index of Multigraphs. Doctoral Thesis, Novosibirsk. (In Russian)
[2] Behzad, M. (1965) Graphs and Their Chromatic Numbers. Ph.D. Thesis, Michigan State University.
[3] Petrosyan, P.A. (2007) Interval Total Colorings of Complete Bipartite Graphs. Proceedings of the CSIT Conference, 84-85.
[4] Zhao, Y. and Su, S. (2017) Cyclically Interval Total Colorings of Cycles and Middle Graphs of Cycles. Open Journal of Discrete Mathematics, 7, 200-217.
https://doi.org/10.4236/ojdm.2017.74018
[5] Vaidya, SK. and Isaac, R.V. (2015) Total Coloring of Some Cycle Related Graphs. IOSR Journal of Mathematics, 11, 51-53.