President Eisenhower's belief that the fall of one nation to Communism would lead to other was

Called the Domino theory (or domino effect)

Explanation:

After World War II, the US and Soviet Union emerged as global superpowers. These two countries had very different plans for a post World War II society. The US wanted to spread democracy and capitalism while the Soviet Union wanted to spread communism. The federal government feared the spread of communism, as it limited individual liberties.

Eisenhower was no exception to this fear. He feared that if one nation fell to communist, nearby nations would fall as well. This is why the US government would adopt a policy of containment. This was based around stopping the spread of communism on a global scale. This policy would result in the US giving money to foreign nations and involvement in civil wars in Korea and Vietnam.

This is called the Domino Effect, and if one fell, he believed other smaller nearby countries would follow.