Abstract
Mosaic graphs, such as the plane representations of the five platonic solids or the three regular and the hyperbolic tesselations of the plane, often are connected with problems in group theory, geometry and especially hyperbolic geometry (see [1], [2]). However, simple combinatorial enumeration problems for mosaic graphs do not seem to have been treated very often in the mathematical literature. In this paper formulas for the numbers of vertices and cells on concentric cycles of (p,q)-tesselations shall be developed.
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References
Coxeter, H. S. M. and Moser, W. O. J. Generators and Realtions for Discrete Groups. Springer-Verlag, Berlin 1957.
Fejes Tóth, L. Reguläre Figuren. Akadémiai Kiadó, Budapest 1965. English translation Regular Figures. Pergamon, New York 1964.
Harary, F. and Harborth, H. “Extremal Animals.” J. Combinatorics Information Syst. Sci. 1 (1976): pp. 1–8.
Robbins, N. “On Fibonacci and Lucas Numbers of the Forms w2 - 1, w3±l.” The Fibonacci Quarterly 19 (1981): pp. 369–373.
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© 1990 Kluwer Academic Publishers
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Harborth, H. (1990). Concentric Cycles in Mosaic Graphs. In: Bergum, G.E., Philippou, A.N., Horadam, A.F. (eds) Applications of Fibonacci Numbers. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-1910-5_13
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DOI: https://doi.org/10.1007/978-94-009-1910-5_13
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-7352-3
Online ISBN: 978-94-009-1910-5
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