Stability of i-connectivity parameters under edge addition

The inclusive edge (vertex, mixed) connectivity of a vertex v is the minimum number of edges (vertices, graph elements) whose removal yields a subgraph in which v is a cutvertex. Stability under edge addition, in which the value of the parameter remains unchanged with the addition of any edge, is investigated. In particular we examine relationships between stability of the inclusive vertex connectivity parameter and stability of the inclusive mixed connectivity parameter, affirming a conjecture posed in [5].