On Vertex-Distinguishing Proper Edge Colorings of Graphs Satisfying the Ore Condition

NSFC [10831001]An edge coloring is proper if no two adjacent edges are assigned the same color and vertex-distinguishing proper coloring if it is proper and incident edge sets of every two distinct vertices are assigned different sets of colors. The minimum number of colors required for a vertex-distinguishing proper edge coloring of a simple graph G is denoted by (chi) over tilde'(G). In this paper, we prove that (chi) over tilde'(G) = 3 and sigma(2)(C) >= n, where sigma(2)(G) = min{d(x) + d(y)| for all xy is not an element of E(G)}