Abstract
An edge coloring is called vertex-distinguishing if every two distinct vertices are incident to different sets of colored edges. The minimum number of colors required for a vertex-distinguishing proper edge coloring of a simple graph G is denoted by \({\chi'_{vd}(G)}\). It is proved that \({\chi'_{vd}(G)\leq\Delta(G)+5}\) if G is a connected graph of order n ≥ 3 and \({\sigma_{2}(G)\geq\frac{2n}{3}}\), where σ 2(G) denotes the minimum degree sum of two nonadjacent vertices in G.
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This work is supported by research grants NSFC (10871119, 10971121) and RFDP (200804220001) of China.
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Liu, B., Liu, G. Vertex-Distinguishing Edge Colorings of Graphs with Degree Sum Conditions. Graphs and Combinatorics 26, 781–791 (2010). https://doi.org/10.1007/s00373-010-0949-2
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DOI: https://doi.org/10.1007/s00373-010-0949-2