Small cycles in the star graph

Elena V. Konstantinova, Alexey N. Medvedev

Research output: Contribution to journalArticlepeer-review


The Star graph is the Cayley graph on the symmetric group Symn generated by the set of transpositions f(12); (13);: :: ; (1n)g. These graphs are bipartite, they do not contain odd cycles but contain all even cycles with a sole exception 4-cycles. We characterize all distinct 6- and 8-cycles by their canonical forms as products of generating elements. The number of these cycles in the Star graph is also given.

Original languageEnglish
Pages (from-to)906-914
Number of pages9
JournalSiberian Electronic Mathematical Reports
Publication statusPublished - 3 Dec 2014
Externally publishedYes


  • Cayley graphs
  • Cycle embedding
  • Product of generating elements
  • Star graph


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