On The Coloring Of Pseudo-Halin Graph

For a 2-connected plane graph G, f0 is a face without chord on its boundary (a cycle), and the vertices degree of V(f0) is at least 3. If all edges on the boundary of a face f0 are removed, G become a tree T in which the degree of vertices except vertices of V(f0) is at least 3,then G is called a Pseudo-Halin graph. G is called to be Halin graph if the degree of every vertex on V(f0) is 3.In this paper, three types of graph coloring for Pseudo-Halin graphs are studied: Incidence coloring, total coloring, complete coloring. The incidence chromatic number of 3-regular Halin graphs is determined by studying its structural property. It is proved that incidence chromatic number of Pseudo-Halin graphs is lower than or equal to + 2.It is proved that Pseudo-Halin graphs with A = 4 or5 has total chromatic number +1 ,and the total coloring number of 3-regular Halin graphs is lower than or equal to 5.At last ,it is proved that the complete coloring number of Pseudo-Halin graphs with A = 4 or5 is lower than or equal to 7.