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

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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 
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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/

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