Vertex-Distinguishing Edge Colorings of Graphs with Degree Sum Conditions |
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Authors: | Bin Liu Guizhen Liu |
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Institution: | 1. School of Mathematics, Shandong University, Jinan, 250100, Shandong, People’s Republic of China
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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 c¢vd(G){\chi'_{vd}(G)}. It is proved that c¢vd(G) £ D(G)+5{\chi'_{vd}(G)\leq\Delta(G)+5} if G is a connected graph of order n ≥ 3 and
s2(G) 3 \frac2n3{\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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