A Generalization of Line Connectivity and Optimally Invulnerable Graphs
Frank T. Boesch, S. Chen · SIAM Journal on Applied Mathematics · 1978
In this work we explore the properties of a simple generalization of $\lambda $, the line connectivity of a graph. This parameter designated by $\lambda _i $ is defined as the minimum number of lines which must be removed from a graph in order that the number of resulting components is greater than i. Several properties of $\lambda _i $ are derived, and the problem of finding graphs which are optimal with respect to $\lambda _i $ is discussed.