Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Twists and Twistability   Metrically homogeneous graphs are connected graphs which, when endowed with
the path metric, are homogeneous as metric spaces. In this paper we introduce
the concept of twisted automorphisms, a notion of isomorphism up to a
permutation of the language. We find all permutations of the language which are
associated with twisted automorphisms of metrically homogeneous graphs. For
each non-trivial permutation of this type we also characterize the class of
metrically homogeneous graphs which allow a twisted isomorphism associated with
that permutation. The permutations we find are, remarkably, precisely those
found by Bannai and Bannai in an analogous result in the context of finite
association schemes.

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The categories of this paper are: hep-th
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The categories of this paper are: patt-sol
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The categories of this paper are: eess
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The categories of this paper are: stat
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The categories of this paper are: hep-ex
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The categories of this paper are: acc-phys
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The categories of this paper are: comp-gas
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The categories of this paper are: supr-con
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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: cmp-lg
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The categories of this paper are: gr-qc
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The categories of this paper are: quant-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: cs
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The categories of this paper are: hep-lat