Can any body help me with this?

Show that if G is a simple graph with n vertices, where each vertex has degree => 1/2*(n-1),then G must be connected.

My answer is,

Total number of degrees of graph are atleast 1/2*n*(n-1)

for complete grah q = 1/2*n*(n-1), where 'q' are total number of edges.

So G is atleast complete graph which means it must be connected.

thnx in advance.