Edge-partitions of graphs and their neighbor-distinguishing index |
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Authors: | Bojan Vučković |
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Institution: | Mathematical Institute, Serbian Academy of Science and Arts, Kneza Mihaila 36 (P.O. Box 367), 11001 Belgrade, Serbia |
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Abstract: | A proper edge coloring is neighbor-distinguishing if any two adjacent vertices have distinct sets consisting of colors of their incident edges. The minimum number of colors needed for a neighbor-distinguishing edge coloring is the neighbor-distinguishing index, denoted by . A graph is normal if it contains no isolated edges. Let be a normal graph, and let and denote the maximum degree and the chromatic index of , respectively. We modify the previously known techniques of edge-partitioning to prove that , which implies that . This improves the result in Wang et al. (2015), which states that for any normal graph. We also prove that when , is an integer with . |
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Keywords: | Neighbor-distinguishing edge coloring Maximum degree Edge-partition |
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