Upper Bounds on the D(β)-Vertex-Distinguishing Edge-Chromatic Numbers of Graphs

摘要

In this paper, let d be the maximum degree of G, we study the upper bounds for the D(β)-vertex-distinguishing edge-chromatic number by probability method and prove that χ′_(β-_(vd))(G) ≤{2 2(β-1)~(1/2)d~(β+2/2), d≥4, β≥4; 8d~(5/2), d≥6, β≥3; 32d~2 d≥4, β≥2.