DMGT

ISSN 1234-3099 (print version)

ISSN 2083-5892 (electronic version)

https://doi.org/10.7151/dmgt

Discussiones Mathematicae Graph Theory

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Discussiones Mathematicae Graph Theory

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Discussiones Mathematicae Graph Theory 23(2) (2003) 383-391
DOI: 10.7151/dmgt.1208

UNDIRECTED AND DIRECTED GRAPHS WITH NEAR POLYNOMIAL GROWTH

V.I. Trofimov

Institute of Mathematics and Mechanics
Russian Academy of Sciences
Ekaterinburg, Russia

To Professor Wilfried Imrich on the occasion of his 60th birthday

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.

Keywords: vertex-symmetric graph; vertex-symmetric directed graph; near polynomial growth; multivalued mapping.

2000 Mathematics Subject Classification: 05C25, 20F65, 37Bxx, 58C06.

References

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[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.
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[5]V. Trofimov, Automorphism groups of graphs as topological groups, Math. Notes 38 (1985) 717-720, doi: 10.1007/BF01163706.
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Received 1 October 2001
Revised 15 February 2002