Regular coverings and parallel products of Farey maps

zbMath1489.05070arXiv2104.03905MaRDI QIDQ5075499

Margaret Rosemary Stanier

Publication date: 16 May 2022

Full work available at URL: https://arxiv.org/abs/2104.03905

zbMATH Keywords

regular mapgraph spectrumHecke groupparallel productmap covering

Mathematics Subject Classification ID

Planar graphs; geometric and topological aspects of graph theory (05C10) Graphs and abstract algebra (groups, rings, fields, etc.) (05C25) Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.) (05C70) Structure of modular groups and generalizations; arithmetic groups (11F06)

Cites Work

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• Non-abelian almost totally branched coverings over the Platonic maps
• Unimodular graphs and Eisenstein sums
• The spectrum of Platonic graphs over finite fields
• Regular maps constructed from linear groups
• Parallel products in groups and maps
• Regular maps and principal congruence subgroups of Hecke groups.
• Families of regular graphs in regular maps
• The spectra of lifted digraphs
• Trivalent expanders, \((\Delta - Y)\)-transformation, and hyperbolic surfaces
• An algebraic approach to lifts of digraphs
• Branched cyclic regular coverings over Platonic maps
• Some elementary Ramanujan graphs
• Petrie polygons, Fibonacci sequences and Farey maps
• Theory of Maps on Orientable Surfaces

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