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recall that the vertex connectivity of a graph is the minimum number of vertices that can be deleted to disconnect it or make it trivial by make it trivial we mean reduce it to a single vertex if you need more of a thorough recap of the definition of vertex connectivity ill leave a link to my lesson on that topic in the description one thing ill remind you about this definition is that the last point about making the graph trivial is just there to account for complete graphs so if a graph has n vertices in order to make it trivial we need to delete all but one vertex as in n minus one vertices now if a graph isnt complete then we wont need to delete that many vertices in order to disconnect it since if a graph isnt complete we could pick two vertices that arent adjacent delete the other n minus two vertices and wed be left with a disconnected graph consisting of two non-adjacent vertices so if a graph isnt complete then we can disconnect it by deleting at most n-2 vertices how
