The relationship between incidence coloring and vertex coloring of graphs

A k-vertex coloring of G is an assignment from k colors to vertex-set V(G) of G such that any two adjacent vertices have different colors. An incidence coloring of graph G is a mapping from I(G) to color set C such that any two neighborly incidences are assigned to different colors. In this paper, two equivalent definitions of incidence graph are firstly given according to the definitions and properties of incidence coloring and vertex coloring. Based on this, some properties of incidence graph will be discussed, and some relationships shall be given between incidence coloring and vertex coloring.