iMac restarting on its own

Theres a good chance nothing is wrong!

Depending on the version of OS-X/MacOS you have installed the OS update service is likely just restarting your system after updating the OS with the maintaince release.

So what is your OS version and I would review the App Stop app looking at the install history to see if it updated your OS.

OK, so your system was not installing any updates and its shutting down on its own during boot.

Then either your power coming into your building has issues or your power supply is failing. Its very rare for the power supply to be stable over long periods then go into a failed condition which is why I would focus on your homes power first.

Check your wall outlet is it properly grounded? Is the polarity correct? many hardware stores have outlet testers which you can plug in to test if they are correctly wired.

You may want to get an electrician in to check your AC breaker panel and the building grounding.

You may need to get a power meter from your power provider to monitor the power over a few days. It plugs into a free outlet and measures the voltage, the sine of the power as well as if your line has surges recording all of it. This is a free service here in the states. Your other option is invest in a good UPS.