On which idea did president eisenhower base his domino theory?

The correct answer is: "containing the spread of communism"

The Domino theory emerged and spread during the 1950s and 1960s. It firmly believed that, when a region fell under communist influence, soon nearby regions would follow the same direction, causing a sort of domino effect.

This argument was used by the US goverment to justify its interventions in third countries and proxy wars (such as the Vietnam conflict), during the Cold War era. US leaders often said they did so to prevent that a certain country, and in turn its whole region, would fall under the influence of the URSS.

doat means to cherish based on the key word fancying and that it is a living thing