Combinatorial Mathematics pp 136-147 | Cite as

# A note on equidistant permutation arrays

## Abstract

Two permutations on *n* elements are at (Hamming) distance μ if they disagree in exactly μ places. An equidistant permutation array is a collection of permutations on *n* elements, every pair of which is at distance μ. A permutation graph *G(n,μ)* is a graph with vertex set comprising all permutations on *n* elements, and edges between each pair of permutations at distance μ. These graphs enable the relevant permutation structure to be visualised; in particular, the cliques correspond to maximal equidistant permutation arrays. We obtain various structural theorems for these graphs, and conjecture several properties for their cliques.

## Keywords

Conjugacy Class Cayley Graph Maximum Clique Complete Subgraph Permutation Graph## Preview

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