乘积图G×P_n和G×C_m的全着色

The Total Coloring of Product Graphs G×P_n and G×G_m

本文证明对乘积图G×Pn 和G×Cm,若G∈C1T,则G×Pn ∈C1T,G×C2m ∈C1T 和G×Cm ∈C1TC2 T;从而证明了乘积图Pr1 ×Pr2 …×Pm ∈C1r,Cr1 ×Cr2 …×Cm ∈C1T ∪C2 T.由此证明了对于这些图全着色猜想成立 .

In this paper,we proved that product graphs G×P n∈C 1 T,G×C 2m ∈C 1 T, and G×C m ∈C 1 T∪C 2 T if G∈C 1 T and then,we proved that P r 1 ×P r 2 …×P m∈C 1 T, when P n is a path with n Vertices,and C r 1 ×C r 2 …C m∈C 1 T∪C 2 T, where C n is a circle with n vertised.Therefore,these graphs the total coloring conjecture is true.