I'm curious whether a simple graph which contains just one vertex is edge k-connected or vertex k-connected.
Edge-k-connectivity: We theoretically can remove any number of edges and it stays connected. The same with vertexes.
Graph satisfies is edge-k-connectivity: IF we remove any k edges -> Graph still satisfies connectivity.
In this case, the left side of implication is never satisfied so it is False. It the left side is False, then the whole implication is True.
EDIT: Graph -> simple graph