Chromatic Numbers of Suborbital Graphs for the Modular Group and the Extended Modular Group by Wanchai Tapanyo, Pradthana Jaipong

“…This research studies the chromatic numbers of the suborbital graphs for the modular group and the extended modular group. We verify that the chromatic numbers of the graphs are 2 or 3. …”
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A Comprehensive Overview on the Formation of Homomorphic Copies in Coset Graphs for the Modular Group by Hanan Alolaiyan, Abdul Razaq, Awais Yousaf, Rida Zahra

“…This work deals with the well-known group-theoretic graphs called coset graphs for the modular group G and its applications. The group action of G on real quadratic fields forms infinite coset graphs. …”
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Cyclotomic equations and square properties in rings by Benjamin Fine

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One-Dimensional Hurwitz Spaces, Modular Curves, and Real Forms of Belyi Meromorphic Functions by Antonio F. Costa, Milagros Izquierdo, Gonzalo Riera

“…We also establish the relation of the meromorphic covers with elliptic functions and show that ℋDp is a quotient of the upper half plane by the modular group Γ(2)∩Γ0(p). Finally, we study the real forms of the Belyi projection ℋDp¯→ℂ^ and show that there are two nonbicoformal equivalent such real forms which are topologically conjugated.…”
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