On The Problem Of Some Graph Coloring

In this paper, four types of graph coloring are discussed: dynamic coloring, incidence coloring, entire coloring and edge-face coloring of planar graphs. Using the combinatorial method of constructibility and the technique of exchanging colors, we present the best upper bounds of dynamic chromatic number of Halin graphs and SP graphs, and determine the dynamic chromatic number of a type of SP graphs, we determine the incidence chromatic number of some Descartes product graphs and some Join graphs . At last we determine the entire coloring number of 1-tree and prove a conjecture of edge-face coloring.