Throughout the paper, G will denote a finite undirected graph without loops or multiple lines. The line-graph L(G) of G is that graph whose point set can be put in one-to-one correspondence with the line set of G, such that two points of L(G) are adjacent if and only if the corresponding lines of G are adjacent. The line-connectivity 2(G) of G is defined to be the smallest number of lines whose removal results in a disconnected graph or the trivial graph. Thus, a nontrivial graph is connected if and only if it has positive line-connectivity. If m < 2(G), then the graph G is said to be m-line-connected. We shall make use of the following simple known propositions: