Adjacent strong edge coloring of graphs Original Research Article

For a graph G(V, E), if a proper k-edge coloring ƒ is satisfied with C(u) ≠ C(v) for uv ∈ E(G), where C(u) = {ƒ(uv) | uv ∈ E}, then ƒ is called k-adjacent strong edge coloring of G, is abbreviated k-ASEC, and χ′as(G) = min{k | k-ASECofG} 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.