Résumé
The Star graph is the Cayley graph on the symmetric group Symn generated by the set of transpositions ((1 i) ε Symn: 2 ≤ i ≤ n). This graph is bipartite and does not contain odd cycles but contains all even cycles with a sole exception of 4-cycles. We denote as (π, id)-cycles the cycles constructed from two shortest paths between a given vertex π and the identity id. In this paper we derive the exact number of (π, id)- cycles for particular structures of the vertex π. We use these results to obtain the total number of 10-cycles passing through any given vertex in the Star graph.
langue originale | Anglais |
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Pages (de - à) | 286-299 |
Nombre de pages | 14 |
journal | Siberian Electronic Mathematical Reports |
Volume | 13 |
Numéro de publication | 1 |
Les DOIs | |
Etat de la publication | Publié - 1 janv. 2016 |
Modification externe | Oui |