Sufficient conditions for maximally restricted edge connected graphs

It is shown in this work that if graph G has degree sequence d 1 ≥ d 2 ≥ ⋯ ≥ d n ≥ 2 with ∑ i = 1 l ( d i + d n − i − 1 ) > l ( n + 2 ) holding for every 1 ≤ l ≤ n / 2 − 2 , then it is 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.