Vertex distinguishing edge coloring of graphs with δ = Δ ≥ n1/3

Abstract

In this paper, we study the vertex distinguishing edge coloring of connected graph with δ(G) = Δ(G) ≥ n/3. The regular graph contains a P_≥3-factor. Denote by P the P_≥3-factor. We can get x'_vd(G) ≤ Δ(G) + 4 by proving G' = G - E(P) has a semi-ude-coloring with k = Δ(G) + 1 colors.