Gobronidze, Mariam; Kipiani, Archil The directed graphs of some functions. (English) Zbl 1458.05091 Trans. A. Razmadze Math. Inst. 174, No. 1, 61-69 (2020). Summary: A description of the digraphs associated with Hamel’s coordinate functions and with some elementary functions is given. Some cardinal invariants of the corresponding mono-unary algebras are found. It is also proved that the digraph of the function tan is an universal graph for the class of digraphs of functions of a certain type. MSC: 05C20 Directed graphs (digraphs), tournaments 08A60 Unary algebras Keywords:functional digraph; Hamel’s coordinate function; basic elementary functions; cardinal invariant PDFBibTeX XMLCite \textit{M. Gobronidze} and \textit{A. Kipiani}, Trans. A. Razmadze Math. Inst. 174, No. 1, 61--69 (2020; Zbl 1458.05091) Full Text: Link References: [1] V. G. Boltyanskii,Hilbert’s Third Problem. (Russian) Izd. Nauka, Moscow, 1977. [2] G. Hamel, Eine Basis aller Zahlen und die unstetigen L¨osungen der Funktiona lgleichungf(x+y) =f(x) +f(y). Math. Ann.60(1905), 459-462. · JFM 36.0446.04 [3] E. Hewitt, K. Stromberg,Real and Abstract Analysis. Springer-Verlag, New York, 1965. · Zbl 0137.03202 [4] A. B. Kharazishvili,P-isomorphisms of binary relations. (Russian)Sakharth. SSR Mecn. Akad. Moambe87(1977), no. 3, 541-544. [5] A. B. Kharazishvili,Questions in the Theory of Sets and in Measure Theory. (Russian) With Georgian and English summaries. Tbilis. Gos. Univ., Tbilisi, 1978. [6] A. B. Kharazishvili,Invariant Extensions of the Lebesgue Measure. (Russian) Tbilis. Gos. Univ., Tbilisi, 1983. [7] A. E. Kipiani, Some combinatorial problems, connected with product-isomorphisms of binary relations.Acta Univ. Carolin. Math. Phys.29(1988), no. 2, 23-25. · Zbl 0682.04002 [8] A. E. Kipiani, Automorphism groups of mono-unary algebras and CH.Georgian Math. J.26(2019), no. 4, 599-610. · Zbl 1448.08002 [9] M. Kuczma,An Introduction to the Theory of Functional Equations and Inequalities. Cauchy’s equation and Jensen’s inequality. PWN, Warszawa-Katowice, 1985. · Zbl 0555.39004 [10] K. Kuratowski, A. Mostowski,Set Theory. North-Holland, Amsterdam, 1967. · Zbl 0165.01701 [11] J. C. Morgan II,Point Set Theory. Monographs and Textbooks in Pure and Applied Mathematics, 131. Marcel Dekker, Inc., New York, 1990. [12] O. Ore,Theory of Graphs. American Mathematical Society Colloquium Publications, vol. XXXVIII American Mathematical Society, Providence, R.I. 1962. · Zbl 0105.35401 [13] W. Sierpinski,Cardinal and Ordinal Numbers. PWN, Warszawa, 1958. · Zbl 0083.26803 [14] S. Ulam, This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.