The easiest way to install Linux OS on your android phone! You do not need to have a rooted phone.
Following this tutorial you would be able to install the following distributions on your phone - Arch, Alpine, Debian, Ubuntu, Kali. You would need to have two apps installed on your device for this tutorial - userland and bvnc viewer - both of which are available for free on the play store.
The userland app makes it very easy to download and set up Linux distribution on your phone.
I have also shown on how you can have a mouse and keyboard interface if you don't have a wireless mouse/keyboard connected to your phone.
If you are looking for a graphic friendly Linux interface I recommend you go with Xfce or lxde.