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An adjacent vertex distinguishing edge-coloring of a graph G is a proper edge-coloring of G such that any pair of adjacent vertices are incident to distinct sets of colors. The minimum number of colors required for an adjacent vertex distinguishing edge-coloring of G is denoted by χ ′ a (G). We prove that χ ′ a (G) is at most the maximum degree plus 2 if G… (More)

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