Abstract
In this paper we define the automorphic H-chromatic index of a graph Γ as the minimum integer m for which Γ has a proper edge-coloring with m colors which is preserved by a given automorphism group H of Γ. After the description of some properties, we determine upper bounds for this index when H is a cyclic group of prime order. We also show that these upper bounds are best possible in a number of instances.
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