| Let G(V,E) be a 2-connected plane graph, f0 a face without chord on its boundary (a cycle) and d(v)≥ 3 for every v ∈ V(f0) . If the graph T obtained from G(V,E) by deleting all edges on the boundary of f0 is a tree of which all vertices v ∈ V\V(f0) satisfy d(.v)≥ 3 , then G(V,E) is called a Pseudo-Halin graph; G(V,E) is said to be Halin-graph iif d(v) = 3 for every v ∈ V(f0) . In this paper,we proved that for any Pseudo-Halin graph with △(G) ≥ 6 , have XC(G) = △(G) + 1 . Where △(G) , XC(G) denote the maximum degree and the complete chromatic number of G, respectively. V(f0) denotes the vertices on the boundary of f0. |
