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2003 | 23 | 2 | 383-391
Tytuł artykułu

Undirected and directed graphs with near polynomial growth

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The growth function of a graph with respect to a vertex is near polynomial if there exists a polynomial bounding it above for infinitely many positive integers. In the paper vertex-symmetric undirected graphs and vertex-symmetric directed graphs with coinciding in- and out-degrees are described in the case their growth functions are near polynomial.
Twórcy
  • Institute of Mathematics and Mechanics, Russian Academy of Sciences, Ekaterinburg, Russia
Bibliografia
  • [1] V. Trofimov, Graphs with polynomial growth, Math. USSR Sb. 51 (1985) 405-417, doi: 10.1070/SM1985v051n02ABEH002866.
  • [2] M. Gromov, Groups of polynomial growth and expanding maps, Publ. Math. IHES 53 (1981) 53-78, doi: 10.1007/BF02698687.
  • [3] L. van den Dries and A. Wilkie, Gromov's theorem on groups of polynomial growth and elementary logic, J. Algebra 89 (1984) 349-374, doi: 10.1016/0021-8693(84)90223-0.
  • [4] A. Veselov, Integrable mapping, Russian Math. Surveys 46 (1991) (5) 1-51.
  • [5] V. Trofimov, Automorphism groups of graphs as topological groups, Math. Notes 38 (1985) 717-720, doi: 10.1007/BF01163706.
  • [6] V. Trofimov, Directed graphs with polynomial growth, in: III Internat. Conf. Algebra (Krasnoyarsk, 1993), Abstracts of Reports, Krasnoyarsk State Univ. and Inst. Math. Siberian Branch Russian Acad. Sci. (Krasnoyarsk, 1993) 334-335 (in Russian).
  • [7] V. Trofimov, Certain asymptotic characteristics of groups, Math. Notes 46 (1989) 945-951, doi: 10.1007/BF01158632.
  • [8] R. Grigorchuk, Semigroups with cancellations of degree growth, Math. Notes 43 (1988) 175-183, doi: 10.1007/BF01138837.
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Bibliografia
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bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1208
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