Undirected and directed graphs with near polynomial growth
Discussiones Mathematicae Graph Theory (2003)
- Volume: 23, Issue: 2, page 383-391
- ISSN: 2083-5892
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topV.I. Trofimov. "Undirected and directed graphs with near polynomial growth." Discussiones Mathematicae Graph Theory 23.2 (2003): 383-391. <http://eudml.org/doc/270249>.
@article{V2003,
abstract = {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.},
author = {V.I. Trofimov},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {vertex-symmetric graph; vertex-symmetric directed graph; near polynomial growth; multivalued mapping},
language = {eng},
number = {2},
pages = {383-391},
title = {Undirected and directed graphs with near polynomial growth},
url = {http://eudml.org/doc/270249},
volume = {23},
year = {2003},
}
TY - JOUR
AU - V.I. Trofimov
TI - Undirected and directed graphs with near polynomial growth
JO - Discussiones Mathematicae Graph Theory
PY - 2003
VL - 23
IS - 2
SP - 383
EP - 391
AB - 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.
LA - eng
KW - vertex-symmetric graph; vertex-symmetric directed graph; near polynomial growth; multivalued mapping
UR - http://eudml.org/doc/270249
ER -
References
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- [2] M. Gromov, Groups of polynomial growth and expanding maps, Publ. Math. IHES 53 (1981) 53-78, doi: 10.1007/BF02698687. Zbl0474.20018
- [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. Zbl0552.20017
- [4] A. Veselov, Integrable mapping, Russian Math. Surveys 46 (1991) (5) 1-51. Zbl0785.58027
- [5] V. Trofimov, Automorphism groups of graphs as topological groups, Math. Notes 38 (1985) 717-720, doi: 10.1007/BF01163706. Zbl0596.05033
- [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. Zbl0702.20002
- [8] R. Grigorchuk, Semigroups with cancellations of degree growth, Math. Notes 43 (1988) 175-183, doi: 10.1007/BF01138837. Zbl0655.20044
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