Most 26" wheels are ISO559 (559mm). The tires that go with the ISO559 rim are decimal (e.g., 1.25" width) not fractional such as the 1 1/8" you mention. The usual road tire closest to 1+1/8" is a 32C. You can find some rims with ISO650C (571mm) but those are much less common. See the rim explanation here
https://www.sheldonbrown.com/rim-sizing.html.