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Some families of total chromatic critical graphs

Wang Zhijian  
In this Paper we introduce the concept of total chromatic matrix, which determines a simple grmplh and one of its total colourings. A graph G is called k-total chromatic critical graph if the total chromatic number of G is k and x2(H)x2(G) holds for any proper subgraph H of G.For every odd integer r 3, some non-trivjal r-total chromatic critical graphs of smallest order are given.
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