I had the same issue with G. They were hitting on my index.html page in my logs, no other SE was doing this. I had to use this code:
RewriteCond %{THE_REQUEST} ^[A-Z]{3,9}\ /index\.html
RewriteRule ^index\.html$
http://www.whateveryourdomainis.com/ [R=301,L]
This did a 301 redirect from index.html to my domain. If your site is hosted on Apache and you have .htaccess file access, you can simply add that line of code in it. It has nothing to do with being on a dedicated server or not.