The l-good-neighbor edge connectivity of graphs

The l -good-neighbor edge connectivity is an useful parameter to measure the reliability and tolerance of interconnection networks. For a graph H with order p and an integer l (l ≥ 0), an edge subset X ⸦ E(H) is called a l-good-neighbor edge-cut if H − X is disconnected and the minimum degree of every component of H − X is at least £. The order of the minimum l-good-neighbor edge-cut of H is called the l-good-neighbor edge connectivity of H, denoted by λ l (H). In this paper, we show λ(H) ≤ λ l+1(H), obtain the bounds of λl (H) when 0 ≤ l ≤ [p-2/2], character some graphs with the small λl (H) and get some results about the Erdös-Gallai-type problem about λl (H).