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Paper   IPM / M / 426
School of Mathematics
  Title:   Uniquely total colorable graphs
1.  S. Akbari
2.  M. Behzad
3.  H. Hajiabolhassan
4.  E. S. Mahmoodian
  Status:   Published
  Journal: Graphs Combin.
  Vol.:  13
  Year:  1997
  Pages:   305-314
  Supported by:  IPM
Uniquely vertex colorable graphs and uniquely edge colorable graphs have been studied extensively by different authors. The literature on the similar problem for total coloring is void. In this paper we study this concept and, among other results, we prove that if a graph GK2 is uniquely total colorable, then χ" (G)=∆+1. Our results support the following conjecture: empty graphs, paths, and cycles of order 3k, k a natural number, are the only uniquely total colorable graphs.

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