In this paper we define the automorphic H-chromatic index of agraph G as the minimum integer m for which G has aproper edge-coloring with m colors which is preserved by a given automorphism group H of G. After the description of some properties, we determine upper bounds for this indexwhen H is a cyclic group of prime order. We also show that these upper bounds are best possible in a number of istances.
On the automorphic chromatic index of a graph
Mazzuoccolo, Giuseppe;
2010-01-01
Abstract
In this paper we define the automorphic H-chromatic index of agraph G as the minimum integer m for which G has aproper edge-coloring with m colors which is preserved by a given automorphism group H of G. After the description of some properties, we determine upper bounds for this indexwhen H is a cyclic group of prime order. We also show that these upper bounds are best possible in a number of istances.
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