Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A bound for the distinguishing index of regular graphs   An edge-colouring of a graph is distinguishing, if the only automorphism
which preserves the colouring is the identity. It has been conjectured that all
but finitely many connected, finite, regular graphs admit a distinguishing
edge-colouring with two colours. We show that all such graphs except $K_2$
admit a distinguishing edge-colouring with three colours. This result also
extends to infinite, locally finite graphs. Furthermore, we are able to show
that there are arbitrary large infinite cardinals $\kappa$ such that every
connected $\kappa$-regular graph has distinguishing edge-colouring with two
colours.

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The categories of this paper are: eess
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The categories of this paper are: alg-geom
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The categories of this paper are: mtrl-th
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The categories of this paper are: patt-sol
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The categories of this paper are: q-bio
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The categories of this paper are: stat
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The categories of this paper are: q-alg
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The categories of this paper are: hep-ph
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The categories of this paper are: q-fin
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The categories of this paper are: adap-org
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The categories of this paper are: gr-qc
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The categories of this paper are: dg-ga
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The categories of this paper are: econ
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The categories of this paper are: comp-gas
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The categories of this paper are: physics
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The categories of this paper are: cmp-lg