A minimal example of building and deploying a blogdown-based website via Travis CI. For more information, please see this section in the blogdown book: https://bookdown.org/yihui/blogdown/travis-github.html. (In short, I don't recommend you use this approach. Consider building your website locally, and deploying through Netlify instead.
David Selby has written a more detailed tutorial with screenshots that you may want to read, too: http://selbydavid.com/2017/06/22/blogdown-travis/.