There is a hypothesis that a non-selfcentric radially-maximal graph of radius r has at least 3r-1 vertices. Using some recent results we prove this hypothesis for r = 4.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1386, author = {Martin Knor}, title = {Minimal non-selfcentric radially-maximal graphs of radius 4}, journal = {Discussiones Mathematicae Graph Theory}, volume = {27}, year = {2007}, pages = {603-610}, zbl = {1142.05023}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1386} }
Martin Knor. Minimal non-selfcentric radially-maximal graphs of radius 4. Discussiones Mathematicae Graph Theory, Tome 27 (2007) pp. 603-610. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1386/
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