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arXiv · 1903.08824

Perfect codes from PGL(2,5) in Star graphs

Ivan Mogilnykh
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Abstract

The Star graph $S_n$ is the Cayley graph of the symmetric group $Sym_n$ with the generating set $\{(1\mbox{ }i): 2\leq i\leq n \}$. Arumugam and Kala proved that $\{π\in Sym_n: π(1)=1\}$ is a perfect code in $S_n$ for any $n, n\geq 3$. In this note we show that for any $n, n\geq 6$ the Star graph $S_n$ contains a perfect code which is a union of cosets of the embedding of $PGL(2,5)$ into $Sym_6$.

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Ivan Mogilnykh. 2019-12-20. Perfect codes from PGL(2,5) in Star graphs. https://arxiv.org/abs/1903.08824

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