  Graph colorings are becoming an increasingly useful family of mathematical
models for a broad range of applications, such as time tabling and scheduling,
frequency assignment, register allocation, computer security and so on. Graph
proper total colorings with additional constrained conditions have been
investigated intensively in the last decade year. In this article some new
graph proper total colorings with additional constrained conditions are
defined, and approximations to the chromatic numbers of these colorings are
researched, as well as some graphs having these colorings have been verified.
