Hi S3, welcome aboard
When you say local, I assume you mean a country search such as vietnam.
Which affects the index in Google.com and local Google search engine?
There are a variety of factors, but my understanding is these are important -
1) Physical location of server
2) Top level domain (.com VS .com.vn)
3) Location of other sites that link to you
4) Content on the site (i.e. address location on contact page)
Will this index in Google.com and local Google search engine affect the frequency of website in search engine results in Google.com and local Google search engine.
If your site is within their index will impact if your site is included in the results.