Undirected and directed graphs with near polynomial growth

V.I. Trofimov

Discussiones Mathematicae Graph Theory (2003)

  • Volume: 23, Issue: 2, page 383-391
  • ISSN: 2083-5892

Abstract

top
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.

How to cite

top

V.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. [1] V. Trofimov, Graphs with polynomial growth, Math. USSR Sb. 51 (1985) 405-417, doi: 10.1070/SM1985v051n02ABEH002866. Zbl0565.05035
  2. [2] M. Gromov, Groups of polynomial growth and expanding maps, Publ. Math. IHES 53 (1981) 53-78, doi: 10.1007/BF02698687. Zbl0474.20018
  3. [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. [4] A. Veselov, Integrable mapping, Russian Math. Surveys 46 (1991) (5) 1-51. Zbl0785.58027
  5. [5] V. Trofimov, Automorphism groups of graphs as topological groups, Math. Notes 38 (1985) 717-720, doi: 10.1007/BF01163706. Zbl0596.05033
  6. [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. [7] V. Trofimov, Certain asymptotic characteristics of groups, Math. Notes 46 (1989) 945-951, doi: 10.1007/BF01158632. Zbl0702.20002
  8. [8] R. Grigorchuk, Semigroups with cancellations of degree growth, Math. Notes 43 (1988) 175-183, doi: 10.1007/BF01138837. Zbl0655.20044

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.