Geodesic
Minimum Edge Cuts in Diameter 2 Graphs
Discussiones Mathematicae. Graph Theory, Tome 39 (2019) no. 2, pp. 605-608.

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Plesnik proved that the edge connectivity and minimum degree are equal for diameter 2 graphs. We provide a streamlined proof of this fact and characterize the diameter 2 graphs with a nontrivial minimum edge cut.
Keywords: edge connectivity, diameter 
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Bickle, Allan; Schwenk, Allen. Minimum Edge Cuts in Diameter 2 Graphs. Discussiones Mathematicae. Graph Theory, Tome 39 (2019) no. 2, pp. 605-608. http://geodesic.mathdoc.fr/item/DMGT_2019_39_2_a21/

[1] G. Chartrand and L. Lesniak, Graphs and Digraphs, 4th Ed. (CRC Press, 2005).

[2] P. Erdős and R.J. Wilson, On the chromatic index of almost all graphs, J. Combin. Theory Ser. B 23 (1977) 255–257. doi:10.1016/0095-8956(77)90039-9

[3] J. Plesnik, Critical graphs of a given diameter, Acta Fac. Rerum Natur. Univ. Comenian. Math. 30 (1975) 71–93.