The automorphic H-chromatic index of a graph G is the minimum integer m for which G has a proper edge-coloring with m colors which is preserved by a given automorphism H of G. We consider the sum and the product of the automorphic H-chromatic index of a graph and its complement. We prove upper and lower bounds in terms of the order of the graph when H is chosen to be either a cyclic group of prime order or a group of order four.
A note on Nordhaus-Gaddum-type inequaliies for the automorphic H-chromatic index of graphs / Ruini, Beatrice. - In: JOURNAL OF GRAPH LABELING. - ISSN 2454-7735. - ELETTRONICO. - 2:(2016), pp. 1-8.
A note on Nordhaus-Gaddum-type inequaliies for the automorphic H-chromatic index of graphs
RUINI, Beatrice
2016
Abstract
The automorphic H-chromatic index of a graph G is the minimum integer m for which G has a proper edge-coloring with m colors which is preserved by a given automorphism H of G. We consider the sum and the product of the automorphic H-chromatic index of a graph and its complement. We prove upper and lower bounds in terms of the order of the graph when H is chosen to be either a cyclic group of prime order or a group of order four.
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