Vertex-distinguishing edge-coloring of graphs with distance between path and circle less than 3 and 4
Tian Jing-jing · Journal of Lanzhou University of Technology · 2008
Let G(V,E) be a connected graph with order ≥3,α,β be positive integers,f be a mapping from E(G) to {1,2,…,α}.If f were an α-proper edge-coloring that C(u)≠ C(v) whenever u,v∈V(G) with 1d(u,v)≤β,then f would be called an α-D(β)-vertex-distinguishing edge-coloring of graph G(shortly,an α-D(β)-VDPEC of G) and the number χ′β-vd(G)=min{α|G has and α-D(β)-VDPEC}would be called the D(β)-vertex-distinguishing edge-chromatic number of G.The vertex-distinguishing proper edge-coloring of graphs with distance between the path and circle less than 3 and 4 was studied and their the D(3)-and D(4)-vertex-distinguishing edge-coloring chromatic number was also obtained.