Selecting vertex display a point with connected edges.
For example, if I select a vertex of cube,
I see an orange point and its connected three edges (edges color is gradient orange).
If I select vertex of object,
can Blender shows only vertex point, not with edges?
I want to see only vertex highlighted.
You will have to change that in the theme. Go to user preferences, and change ‘edge select’ to black. But note well that when in edge mode for example you will have selected but inactive edges also turned off! So you may not want that at all. I have not heard of this being a problem before… Maybe you just want to make the ‘vertex select’ a much brighter and different color than ‘edge select’, e.g my vertices are Blue and my edges are orange, or maybe make the vertex size bigger (in the same place).