Power connections to UNO Vin pin

I have a project running that requires a stepper (the 28BYJ) and I am providing 9v / 1A to the ULN 2003 board. Can I take a feed from that same 12v supply to the Vin pin on the Ardunio?
Thanks for any advice,

what type of Arduino? is it powering anything? what's connected on this Arduino that will draw current?

at 12V you keep the regulator pretty busy contributing to climate change by dissipating (12 - 5) = 7V x the amp you consume as heat... There is not a lot of margin before the regulator overheats and shuts down.

providing 9V would already be better (3V less to step down)

Its an Arduino UNO. Apart from the stepper which has its own supply, I have three LDRs using 10K pull-up resistors on A0-A2, a Hall device with 10K pull-up on pin3 and a couple of LEDs on pin 4. Everything works just fine with a regular USB charger running the Arduino and the 9v supply for the stepper. I just wondered if I can get rid of the USB charger and run the Arduino from the 9v supply using the Vin pin.

If you haven't left out any details, the answer is yes, you can. How much current on your "couple of LEDs"? I hope you have current limiting resistors there?

Two alternating LEDs with 560ohm resistors. I think this should be OK.
I just wasn't sure what exactly the Vin pin was for, its just an alternative to the so-called "barrel" connector - right?

Yes, but depending on the model, there may be a diode between the barrel jack and VIN. UNO does.

OK I will check - thanks!

You can get a "seat of the pants" idea of how well that works, by putting your fingers (carefully!) on the voltage regulator IC. If you can fry an egg on it, maybe it's not such a good idea.

The barrel jack is the 'safest' implementation and it doesn't take up any limited header space.

So all is well, the regulator was barely warm after 15 mins of operation!