A Characterization for the Neighbor-Distinguishing Index of Planar Graphs

Symmetry, such as structural symmetry, color symmetry and so on, plays an important role in graph coloring. In this paper, we use to study the characterization for neighbor-distinguishing index of planar graphs. Let G be a simple with no isolated edges. The edge coloring is proper that any two adjacent vertices admit different sets consisting colors their incident χa′(G) smallest number G. It was conjectured if connected at least three G≠C5, then χa′(G)≤Δ+2. show maximum degree Δ≥13, Δ≤χa′(G)≤Δ+1, and, further, χa′(G)=Δ+1 only contains degree.