Geodesic
Small cycles in the star graph
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 11 (2014), pp. 906-914

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The Star graph is the Cayley graph on the symmetric group $Sym_n$ generated by the set of transpositions $\{(1 2),(1 3),\ldots,(1 n)\}$. 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.
Keywords: Cayley graphs; Star graph; cycle embedding; product of generating elements. 
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     author = {Elena V. Konstantinova and Alexey N. Medvedev},
     title = {Small cycles in the star graph},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {906--914},
     publisher = {mathdoc},
     volume = {11},
     year = {2014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2014_11_a55/}
}
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Elena V. Konstantinova; Alexey N. Medvedev. Small cycles in the star graph. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 11 (2014), pp. 906-914. http://geodesic.mathdoc.fr/item/SEMR_2014_11_a55/