This paper defined the star-edge coloring and star chromatic index x′_s(G),and proved that if G is a graph withΔ≥7 then x′_s(G)≤[16(Δ-1)3/2].

Furthermore,a simple and feasible star-edge coloring method is also put forward.

introduced the concept of star-edge coloring of graphs, a star-edge coloring of graph G is a proper edge coloring of G such that any path of length 4 in G is not bicolored.

This paper discusses the properties of the critical graphs about the star colorings, and obstain several necessary conditions and sufficent conditions how to judge that a graph is critical graph about the star coloring.

A k-proper total coloring of graph G is called the star total coloring of G,if the Coloring of the vertices and edges of any path of length 2 in G are all different,the least number of k spanning over all k-star-total-colorings of G is called the star total chromatic number of G.

An upper bound on the star chromatic index of graphs withΔ≥7;

The list strong edge coloring of graphs with Δ(G)=3;

The strong edge coloring of graphs with Δ(G)=4;