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AI Summary & Key Takeaways
AI Insight⚡ TL;DR(Too Long; Didn't Read)
Finally, we examine the connectivity of the subgraph F u,N and show that it is connected if and only if N ≤ 2 .
📌 3 Key Takeaways
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Objective & Hypothesis:In this paper, we investigate suborbital graphs formed by the action of Γ 2 which is the group generated by the second powers of the elements of the modular group Γ on Q ˆ .
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Key Findings & Data: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.
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Conclusion & Impact:Finally, we examine the connectivity of the subgraph F u,N and show that it is connected if and only if N ≤ 2 .
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Modular group · Group action · Suborbital graphs
Abstract
In this paper, we investigate suborbital graphs formed by the action of Γ 2 which is the group generated by the second powers of the elements of the modular group Γ on Q ˆ . 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 ≤ 2 .
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Cite This Article
Güler, B. Ö., Beşenk, M., Kesicioğlu, Y., Değer, A. H. (2015). Suborbital graphs for the group $\Gamma^2$. Hacettepe Journal of Mathematics and Statistics, Volume: 44 Issue: 5. https://ajindex.com/articles/1403234