Suborbital graphs for the group Gamma^{2}

GÜLER B. Ö., BEŞENK M., Kesicioglu Y., DEĞER A. H.

HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS, vol.44, no.5, pp.1033-1044, 2015 (SCI-Expanded, Scopus, TRDizin)

  • Publication Type: Article / Article
  • Volume: 44 Issue: 5
  • Publication Date: 2015
  • Journal Name: HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.1033-1044
  • Karadeniz Technical University Affiliated: Yes

Abstract

In this paper, we investigate suborbital graphs formed by the action of $\Gamma^{2}$ which is the group generated by the second powers of the elements of the modular group $\Gamma$ on $\hat{\mathbb{Q}}$. Firstly, conditions for being an edge, self-paired and paired graphs are provided, then we give necessary and sufficient conditions for the suborbital graphs to contain a circuit and to be a forest. Finally, we examine the connectivity of the subgraph $F _{u,N}$ and show that it is connected if and only if $N\leq2$.