This is the (finite) covering problem in the plane. According to Boroczky's book "Finite packing and covering", the answer is only known (provably) up to $k = 10$, due to the work of K. Bezdek and G. Fejes Toth. I don't know if the solutions are a famous sequence of geometric graphs.
           http://mathworld.wolfram.com/images/eps-gif/DiskCoveringProblem5_800.gif _{(Image from MathWorld added by J.O'Rourke)}

This is the (finite) covering problem in the plane. According to Böröczky's book Finite packing and covering, the answer is only known (provably) up to $k = 10$, due to the work of K. Bezdek and G. Fejes Toth. I don't know if the solutions are a famous sequence of geometric graphs.

           _{(Image from MathWorld added by J.O'Rourke (source))}

This is the (finite) covering problem in the plane. According to Boroczky's book "Finite packing and covering", the answer is only known (provably) up to $k = 10$, due to the work of K. Bezdek and G. Fejes Toth. I don't know if the solutions are a famous sequence of geometric graphs.

This is the (finite) covering problem in the plane. According to Boroczky's book "Finite packing and covering", the answer is only known (provably) up to $k = 10$, due to the work of K. Bezdek and G. Fejes Toth. I don't know if the solutions are a famous sequence of geometric graphs.
           http://mathworld.wolfram.com/images/eps-gif/DiskCoveringProblem5_800.gif _{(Image from MathWorld added by J.O'Rourke)}