# 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

top- [1] V. Trofimov, Graphs with polynomial growth, Math. USSR Sb. 51 (1985) 405-417, doi: 10.1070/SM1985v051n02ABEH002866. Zbl0565.05035
- [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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