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December 2017 - Solution
The idea in this challenge is to connect a chain of (almost) cliques and carefully make the graph nine-regular.
As an example solution, we present here the drawing of Alper Halbutogullari (thanks!).
Thanks also to Bert Dobbelaere, for pointing out the paper Smallest Regular Graphs of Given Degree and Diameter and to Vladimir M. Milovanović for telling us about the paper Graphs of Maximum Diameter.