Small cycles in the star graph

Elena V. Konstantinova; Alexey N. Medvedev

Small cycles in the star graph

Elena V. Konstantinova, Alexey N. Medvedev

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Résumé

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.

langue originale	Anglais
Pages (de - à)	906-914
Nombre de pages	9
journal	Siberian Electronic Mathematical Reports
Volume	11
Etat de la publication	Publié - 3 déc. 2014
Modification externe	Oui

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Contient cette citation

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title = "Small cycles in the star graph",

abstract = "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.",

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AU - Konstantinova, Elena V.

AU - Medvedev, Alexey N.

PY - 2014/12/3

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N2 - 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.

AB - 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.

KW - Cayley graphs

KW - Cycle embedding

KW - Product of generating elements

KW - Star graph

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M3 - Article

AN - SCOPUS:84986910209

SN - 1813-3304

VL - 11

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JO - Siberian Electronic Mathematical Reports

JF - Siberian Electronic Mathematical Reports

ER -

Small cycles in the star graph

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