Abstract
In this paper, we shall first prove that for a Halin graph G, 4 ≤ χT(G) ≤ 6, where χT(G) is the vertex-face total chromatic number of G. Second, we shall establish a sufficient condition for a Halin graph to have a vertex-face total chromatic number of 6. Finally, we shall give a necessary and sufficient condition for a Halin graph to have a vertex-face total chromatic number of 4 and describe a way of assigning the four colors to such graphs. © 1997 John Wiley & Sons, Inc. Networks 30:167–170, 1997
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