a vertice is not an object.., so makes a bad example.., its an element of one.., an object is made of vertices connected together.., making edges.., edges are connected together to make faces.., faces are connected together to make objects.
are you using polys or nurbs..??
you could be in hull mode, there could be many reasons for this.., if you do a screen grab and load it onto this thread.., me or someone will give you a definitive answer.
ExtrudedDingus has given you good advice none the less.., all good
take it easy and life will be easy