3-正则Halin图的完备染色

omplete coloring of plane graphs is the simultaneously coloring of vertices, edges and faces, such that no two adjacent or incident elements receive the same color. The complete chromatic number χC(G) of G is the least number of colors such that the complete coloring is correct. For simple planar graphs, the complete coloring conjecture is: χC(G)l≤△(G)+4, where △(G) is the maximum degree of G. In the paper, we study the complete coloring of 3-regular Halin graphs. We propose a procedure for completely coloring an 3-regular Halin graph which is not a wheel graph. By this, we can easily determine that χC(G)=6, where G(≠W4) is a 3-regular Halin graph. Furthermore, this implies that the complete coloring of a 3-regular Halin graph can be solved by computer.