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.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1208, author = {V.I. Trofimov}, title = {Undirected and directed graphs with near polynomial growth}, journal = {Discussiones Mathematicae Graph Theory}, volume = {23}, year = {2003}, pages = {383-391}, zbl = {1056.05079}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1208} }
V.I. Trofimov. Undirected and directed graphs with near polynomial growth. Discussiones Mathematicae Graph Theory, Tome 23 (2003) pp. 383-391. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1208/
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