Sufficient conditions for maximally restricted edge connected graphs

It is shown in this work that if graph GG has degree sequence d1≥d2≥⋯≥dn≥2d1≥d2≥⋯≥dn≥2 with ∑i=1l(di+dn−i−1)>l(n+2) holding for every 1≤l≤n/2−21≤l≤n/2−2, then it is λ′λ′-optimal. The lower bound on the degree-summation is exemplified sharp. This observation generalizes the corresponding results of Bollobás on maximal edge connectivity of graphs.