Suppose there exists a connected group of Facebook friends. That is, there is a way to reach every person from every other person through some traversal of friendships. Additionally, there is no cycle of friendships (ex. we would not have the following case: 1 is friends with 2, who is friends with 3, who is friends with 1). Suppose that some person u in this group has at least d friends. Prove that there exists at least d people in this group with exactly 1 friend. Hint: Think about what specific type of graph this is based on the definition!