I wanted a black wallpaper because with an AMOLED screen, if you turn OFF the pixels then they use less power so the battery should last longer.
So, I created a 1080x1920 image and filled it with black (in Windows Paint), saved it and downloaded it to my phone. Sure enough - when I selected it I had a black wallpaper. Terrific. Then I scaled the image down to 135 x 240, downloaded this to the phone and set this as the wallpaper and this worked OK too. It obviously tiled the image or blew it up to match the required size. So, by doing this I waste less of the memory on my SD card than if I used a full 1080x1920 image.
So, just for the fun of it I uploaded a cropped photo which was 600x600. The phone took the photo and expanded it so that the photo filled the whole screen's height which meant that it cropped the left and right sides of the image and expanded the resulting 337x 600 image to fill the whole screen.
So ...
There is no point using an image with a higher resolution than 1080x1920 for the wallpaper as this is the native resolution of the screen and you would just be wasting space on your phone but you can scale this size down if you wanted to use less space on your phone for the original image (eg 540x960, 360x640, 270x480, 180x320 or 108x192 or 54x96 or even 27x48)
So now, because I just want a black wallpaper I use the 27x48 pixel size.