On graphs with equal edge connectivity and minimum degree

The note contains some conditions on a graph implying that the edge connectivity is equal to the minimum degree. One of these conditions is that if d₁?d₂???d_n is the degree sequence then ∑^l_l?1(d₁+d_n?1)>In?1 for $\text{1 ? l? min {}\text{n}\text{2?1}\text{, d}{}_{\mathrm{n}}\text{}}$.