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

Research output: Contribution to journalArticlepeer-review

Abstract

The Star graph Snis the Cayley graph of the symmetric group Sym„ with the generating set {(1 i) : 2 < i < n}. Arumugam and Kala proved that {π Є Sym„: π(1) = 1} is a perfect code in Snfor any n, n > 3. In this note we show that for any n, n > 6 the Star graph Sncontains a perfect code which is the union of cosets of the embedding of PGL(2,5) into Sym6.

Original languageEnglish
Pages (from-to)534-539
Number of pages6
JournalСибирские электронные математические известия
Volume17
DOIs
Publication statusPublished - 2020

Keywords

  • Cayley graph
  • efficient dominating set
  • perfect code
  • projective linear group
  • Star graph
  • symmetric group
  • CAYLEY-GRAPHS

OECD FOS+WOS

  • 1.01 MATHEMATICS

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