given a undirected graph ( n nodes , m edges ) , find minimum no. of nodes to remove for making graph completely disconnected ?

constraints — n upto 1000

A greedy way could be start removing the maximum degree nodes untill graph becomes disconnected, is there a proof it would work ?

also i think its related to menger's algorithm , but that gives vertex cut for making 2 nodes disconnected , here we have to disconnect all nodes from each other..