Let $mathcal{P}_0(A_n), widetilde{mathcal{P}}_0(A_n), mathcal{T}_0(A_n)$ and $mathcal{O}_0(A_n)$ be respectively the proper power graph, the proper quotient power graph, the proper type graph and the proper order graph of the alternating group $A_n$, for $ngeq 3.$ We determine number and typology of the components of those graphs. In particular, we prove that the power graph $mathcal{P}(A_n)$ is $2$-connected if and only if the type graph $mathcal{T}(A_n)$ is $2$-connected, if and only if either $n = 3$ or none of $n, n-1, n-2, rac{n}{2}$ and ${rac{n-1}{2}}$ is a prime.

On some graphs associated with the finite alternating groups / D. Bubboloni; M. A. Iranmanesh; S.M.Shaker. - In: COMMUNICATIONS IN ALGEBRA. - ISSN 0092-7872. - STAMPA. - 45:(2017), pp. 5355-5373. [10.1080/00927872.2017.1307381]

On some graphs associated with the finite alternating groups

BUBBOLONI, DANIELA;
2017

Abstract

Let $mathcal{P}_0(A_n), widetilde{mathcal{P}}_0(A_n), mathcal{T}_0(A_n)$ and $mathcal{O}_0(A_n)$ be respectively the proper power graph, the proper quotient power graph, the proper type graph and the proper order graph of the alternating group $A_n$, for $ngeq 3.$ We determine number and typology of the components of those graphs. In particular, we prove that the power graph $mathcal{P}(A_n)$ is $2$-connected if and only if the type graph $mathcal{T}(A_n)$ is $2$-connected, if and only if either $n = 3$ or none of $n, n-1, n-2, rac{n}{2}$ and ${rac{n-1}{2}}$ is a prime.
2017
45
5355
5373
D. Bubboloni; M. A. Iranmanesh; S.M.Shaker
File in questo prodotto:
File Dimensione Formato  
Printed-version-On some graphs associated with the finite alternating groups.pdf

Accesso chiuso

Descrizione: articolo
Tipologia: Pdf editoriale (Version of record)
Licenza: Tutti i diritti riservati
Dimensione 553.44 kB
Formato Adobe PDF
553.44 kB Adobe PDF   Richiedi una copia

I documenti in FLORE sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificatore per citare o creare un link a questa risorsa: https://hdl.handle.net/2158/1089865
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 22
  • ???jsp.display-item.citation.isi??? 19
social impact