Relation between k and k-1 edge connected graph

Question

Is every k connected graph is k-1 connected or the reverse? I always get confused. Can someone explain with the help of an example.

Comments

i did nt get ur question

Answer 1

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. 
 

Comments

Yes. Thanks.  reason is : if removing many vertices cannot disconnect the graph, then you  have no hope of disconnecting the graph by removing fewer vertices.

But this is not the only definition generally used. There are others and in those cases above conjecture is not true.