Задача 20.

*1) Show that a regular graph with valency $k$ and diameter $2$ cannot have more than $k^2+1$ vertices. 2) Give examples of Moore graph for $k=1,2,3$. 3) Is there a Moore graph with $k=7$? 4**) Is there a Moore graph with $k=5$? 5) Show that there is no Moore graph for other $k$'s.