k edge connected graph : A graph that is connected remains connected when less than k number of edges are removed is called a k edge connected graph.
For example
According to the definition a triangle is also a 1 edge connected graph but not 3 edge connected graph because removing 2 edges will disconnect it. So, it should be "every k connected graph is also k-1 connected graph" but the reverse is not true.
Correct me if i am wrong,anyone.