what is the minimal hop-count for a undirected (directed) graph (of size N) restricted to the number of edges per node (k)?
Clearly, it can be possible to build a graph with N and k in infinite ways, what I'm interested in is the maximum hops for an optimal graph.
For example, if I have a graph with N=N and k=N-1 then the solution I'm looking for is x=1. The hop-count for the best possible graph (all nodes are directly connected to any other) is one hop for each node.
I hope I make myself clear :), sorry if I don't.
The solution will look something like that:
x=N/k , with larger k and const. N, x needs to get larger, and vice versa.
Thanks a lot for the help. Please be nice if this is too unclear, easy, or redundant.