Google recently released a new feature to show if a site is “mobile friendly”. Google’s new ‘Mobile-friendly’ label that may be included in mobile search results for websites that qualify for it without the website owner doing any additional work. Here is a screen shot of a search result for Mashable.com
Any website owner can check their site using this free tool from Google at https://search.google.com/test/mobile-friendly
Both mobile optimized sites or fully responsive sites get a thumbs up from Google. Here are two screen shots: one from a site that converts this site to a mobile site, and the other from the fully responsive version on this site.