Adjacent strong edge coloring of graphs

For a graph G(V, E), if a proper k-edge coloring ? is satisfied with C(u) ≠ C(v) for uv ∈ E(G), where $\text{C(u) = {?(uv) | uv ∈ E}}$, then ? is called k-adjacent strong edge coloring of G, is abbreviated k-ASEC, and χ′_as(G) = min{k | k-ASEC of G} is called the adjacent strong edge chromatic number of G. In this paper, we discuss some properties of χ′_as(G), and obtain the χ′_as(G) of some special graphs and present a conjecture: if G are graphs whose order of each component is at least six, then χ′_as(G) ≤ Δ(G) + 2, where Δ(G) is the maximum degree of G.