Geodesic
On critical and cocritical radius edge-invariant graphs
Discussiones Mathematicae. Graph Theory, Tome 28 (2008) no. 3, pp. 393-418

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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.
Keywords: extremal graphs, radius of graph 
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     author = {Vacek, Ondrej},
     title = {On critical and cocritical radius edge-invariant graphs},
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Vacek, Ondrej. On critical and cocritical radius edge-invariant graphs. Discussiones Mathematicae. Graph Theory, Tome 28 (2008) no. 3, pp. 393-418. http://geodesic.mathdoc.fr/item/DMGT_2008_28_3_a1/