It is proved that if G is a (+1)-colorable graph, so are the graphs G×Pn and C×Cn, where Pn and Cn are respectively the path and cycle with n vertices, and the maximum edge degree of the graph. The exact chromatic numbers of the product graphs and are also presented. Thus the total coloring conjecture is proved to be true for many other graphs. It is proved that if G is a (+1) -colorable graph, so are the graphs G × Pn and C × Cn, where Pn and Cn are the path and cycle with n vertices, and the maximum edge degree of the graph The exact chromatic numbers of the product graphs and are also presented. Thus the total coloring conjecture is proved to be true for many other graphs.