Geodesic
Undirected and directed graphs with near polynomial growth
Discussiones Mathematicae. Graph Theory, Tome 23 (2003) no. 2, pp. 383-391

Voir la notice de l'article provenant de la source Library of Science

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.
Keywords: vertex-symmetric graph, vertex-symmetric directed graph, near polynomial growth, multivalued mapping 
Trofimov, V. Undirected and directed graphs with near polynomial growth. Discussiones Mathematicae. Graph Theory, Tome 23 (2003) no. 2, pp. 383-391. http://geodesic.mathdoc.fr/item/DMGT_2003_23_2_a11/
@article{DMGT_2003_23_2_a11,
     author = {Trofimov, V.},
     title = {Undirected and directed graphs with near polynomial growth},
     journal = {Discussiones Mathematicae. Graph Theory},
     pages = {383--391},
     year = {2003},
     volume = {23},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DMGT_2003_23_2_a11/}
}
TY  - JOUR
AU  - Trofimov, V.
TI  - Undirected and directed graphs with near polynomial growth
JO  - Discussiones Mathematicae. Graph Theory
PY  - 2003
SP  - 383
EP  - 391
VL  - 23
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/DMGT_2003_23_2_a11/
LA  - en
ID  - DMGT_2003_23_2_a11
ER  - 
%0 Journal Article
%A Trofimov, V.
%T Undirected and directed graphs with near polynomial growth
%J Discussiones Mathematicae. Graph Theory
%D 2003
%P 383-391
%V 23
%N 2
%U http://geodesic.mathdoc.fr/item/DMGT_2003_23_2_a11/
%G en
%F DMGT_2003_23_2_a11

[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.