Sir you said that vertex connectivity should be n-1 for a complete graph so then it degrades down to a single vertex which is still connected right ?
So here also you cant disconnect complete graph
We can not disconnect the complete graph. That’s why vertex connectivity is defined as n-1 in the literature. you can assume it as an exception.
So,In case of complete graph which is an exception we will end up in single vertex always and we should consider single vertex as a disconnect graph?
No single vertex is always a connected graph.
Sir Every k-connected graph is k-1 connected, can you tell me is this true or false?
A graph G is said to be k-connected (or k-vertex connected, or k-point connected) if there does not exist a set of k-1 vertices whose removal disconnects the graph, i.e., the vertex connectivity of G is >=k
In such graph there doesn’t exist a set of vertices of k-2 vertices whose removal disconnects the graph. So obviously it is k-1 connected too.