We verify two conjectures(the famous total coloring conjecture and the more recent adjacent vertex-distinguishing total coloring conjecture) for the class of twisted cubes by explicit calculation of the respective parameters.
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Behzad Mehdi.Graphs and their chromatic numbers[D].East Lansing:Michigan State University,1965.
Vizing Vadim Georgievich.Some unsolved problems in graph theory[J].Uspekhi Mat Nauk,1968,23:117-134.
Zhang Zhongfu,Chen Xiang’en,Li Jingwen.On the adjacent vertex-distinguishing total coloring of graphs[J].Science in China Ser A Mathematics,2005,48:289-299.
Chen Meirun,Guo Xiaofeng,Li Hao,et al.Total chromatic number of generalized Mycielski graphs[J].Discrete Mathematics,2014,334:48-51.
Chen Meirun,Zhai Shaohui.Total and adjacent vertex-distinguishing total chromatic numbers of augmented cubes[J].Ars Combinatorics,2014,114:87-96.
Huang Wentzeng,Tan Jimmy,Hung Chunnan,et al.Fault-tolerant hamiltoncity of twisted cubes[J].Journal of Parallel and Distributed Computing,2002,62:591-604.