Contrary to popular belief, a cemetery is the last place in which I would expect a so-called "ghost" to be seen. Even so, there are innumerable accounts of ghostly appearances in cemeteries. Several people have related their stories of the vanishing little girl in Anfield cemetery in Liverpool.
One sunny afternoon whilst on our way to my grandad's grave, me and my nan came face to face with a slightly built little girl of around the age of nine, who stood in front of us smiling, before completely disappearing.
The young girl had walked between the gravestones and had lingered for a few moments by a grave with nothing more than a leaning marble cross to mark its position.
The grave was overgrown, and looked as though nobody had visited it for years. On closer inspection my nan read the inscription on the cross.
"Our Becky, tragically taken from us at the age of nine." We both felt an icy shiver pass though us, and were overwelmed with sadness, when we realised that we had come face to face with Becky the smiling little girl.
I couldn't stop thinking of our experience, and when we finaly got home I was so freaked out about it, I walked into the kichen and was expecting to see her sitting at the table and say "Oh hello again, what's for dinner?." The next day, when the girls came home from Vicki's house thay didn't believe us.
So I decided to put it on this site.
Like sotherntk said, the little girl didn't want to be forgotten, especially because of the way she died. My suggestion to you would be that the next time you go to visit your grandfather's grave, bring some flowers for the little girl and leave it at her grave. Also, if I read correctly in your story, the area around her grave was messy. If you can, cleanup it up a little for her. It might help.