Some lattice theoretical results on non-Euclidean graphs

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Gökcan İ., Değer A. H.

ANALELE STIINTIFICE ALE UNIVERSITATII OVIDIUS CONSTANTA, SERIA MATEMATICA, cilt.34, sa.1, ss.129-150, 2026 (SCI-Expanded, Scopus)

• Yayın Türü: Makale / Tam Makale
• Cilt numarası: 34 Sayı: 1
• Basım Tarihi: 2026
• Doi Numarası: 10.2478/auom-2026-0007
• Dergi Adı: ANALELE STIINTIFICE ALE UNIVERSITATII OVIDIUS CONSTANTA, SERIA MATEMATICA
• Derginin Tarandığı İndeksler: Scopus, Science Citation Index Expanded (SCI-EXPANDED), MathSciNet, zbMATH, Directory of Open Access Journals
• Sayfa Sayıları: ss.129-150
• Karadeniz Teknik Üniversitesi Adresli: Evet

Özet

This paper develops a unified framework connecting lattice theory

and suborbital graphs, with particular focus on Farey graph. By equip-
ping the Farey graph with lattice structures, we reveal new combina-
torial and algebraic properties. Essential element graphs, Hasse dia-
grams, and integer sequences for vertices and edges are systematically

explored. This study distinguishes itself from previous studies by ex-
panding proofs, consolidating definitions, and providing illustrative ex-
amples. Our results demonstrate how a lattice perspective can enrich

theoretical and applied research in number theory, geometry, and net-
work science.