can a mac mini be connected to an iMac?

You can connect any of these older iMac models to another Mac from 2019 or earlier for use as an external display. Learn how to identify your iMac model.

• 27-inch iMac models introduced in 2009 and 2010: Use a Mini DisplayPort cable to connect your iMac to a Mini DisplayPort or Thunderbolt or Thunderbolt 2 port on the other Mac.
• All iMac models introduced in 2011, 2012, 2013, and mid 2014: Use a Thunderbolt cable to connect your iMac to a Thunderbolt or Thunderbolt 2 port on the other Mac. If the other Mac uses Thunderbolt 3, you can use the Apple Thunderbolt 3 (USB-C) to Thunderbolt 2 Adapter with your cable.

Target display mode requires macOS High Sierra or earlier on the iMac used as the external display. It does not work with macOS Mojave or later.

You can also connect for file sharing etc, using Wifi or Ethernet.

What are you attempting to achieve by connecting them? Also, Mac mini's have been available for many years and iMacs for over 20 years so don't assume we have any clue which ones you own or the versions of Mac OS installed. I would recommend reading Writing an effective Apple Support Communities Question before re-asking your questions.

Any luck yet?