What is the difference between 没有+V. and 没+V.?
[沒+ X(v)]  is the negative form of [有+ X(v)] (replace 有 with 沒)


Example:

[沒殺人] (did not kill someone) 

[有殺人]( have killed someone / did kill someone) 

*Replace 有 with 沒


  [沒有+ X(v)] is  also the negative form of [有+X(v)] (add 沒 before 有)


Example: 

[沒有殺人] (did not kill someone) 

[有殺人]( have killed someone / did kill someone) 

*Add 沒 before 有

Simply put,  沒 can be used as the shortened form of 沒有 

You can also see it as:  "to turn [有+ X(v)] into negative, you can either replace 有 with 沒 or add 沒 before 有"