For every positive integer $n$ construct a graph G on $n$ vertices in which the number of different local edge-connectivity values is at least $n-1$. I know that for a complete graph $K_n), \lambda(K_n)=n-1$, my problem is how to construct graphs whose different local edge-connectivity
is at least $n-1$. Can we use $K_n$ to construct this kind of graph or do we have other means to generalize it? Thanks for your cooperation.