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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 Fu,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 Γ2 which is the group generated by the second powers of the elements of the modular group Γ on Qˆ.
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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 Fu,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 Γ2 which is the group generated by the second powers of the elements of the modular group Γ on Qˆ. 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 Fu,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., KESİCİOĞLU, Y., DEĞER, A. H. (2015). Suborbital graphs for the group $\Gamma^2$. Hacettepe Journal of Mathematics and Statistics, Cilt: 44 Sayı: 5, 1033–1044. https://ajindex.com/articles/929274