>>You're talking about NFC (Near Field Communications). Newer OS's have API's:
>>
>>http://developer.android.com/reference/android/nfc/package-summary.html
>>https://software.intel.com/en-us/articles/using-nfc-from-windows-8-applications
>
>Thanks, on App Store, only two apps are found on those words. One is NFC Actions but it does not look like this is one.
>
>NFC, however, returns more results.
>
>Still not sure exactly what should be looked for here to obtain something workable. I do not even know if something like that already exists to ease the process of adding a recognized LinkedIn profile from another phone and send a connection request.

I'm not sure what you want to do. If you want your own App to implement NFC then you need to write the code for the relevant interface. The links I provided contain documentation.