The concepts of critical and cocritical radius edge-invariant graphs are introduced. We prove that every graph can be embedded as an induced subgraph of a critical or cocritical radius-edge-invariant graph. We show that every cocritical radius-edge-invariant graph of radius r ≥ 15 must have at least 3r+2 vertices.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1415, author = {Ondrej Vacek}, title = {On critical and cocritical radius edge-invariant graphs}, journal = {Discussiones Mathematicae Graph Theory}, volume = {28}, year = {2008}, pages = {393-418}, zbl = {1173.05017}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1415} }
Ondrej Vacek. On critical and cocritical radius edge-invariant graphs. Discussiones Mathematicae Graph Theory, Tome 28 (2008) pp. 393-418. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1415/
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