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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.
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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. 
 

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