B) Any two people can get to know each other through one or more introductions from friends.
c)G = & lt； V, E> is a simple undirected graph with n(≥3) nodes, each node represents a person, and two nodes are adjacent if and only if the corresponding person is a friend. If any two people know the remaining n-2 people together, it means that there are deg(u)+deg(v)≥n-2 in any two nodes U and V in Figure G, and the remaining n-2 nodes must be adjacent to U or V, which proves that there must be deg(u)+deg(v)≥n- 1 under this condition.
(1) if u is adjacent to v, deg (u)+deg (v) ≥ 2+n-2 = n > n- 1 .
(2) if u and v are not adjacent, if deg(u)+deg(v)≥n-2, and V-{u, v} has exactly n-2 nodes (n-3, so V-{u, V} ≦{φ}, where each node can only be connected to one of u and v, at this time. Therefore, for any u, v must have deg (u)+deg (v) >: N-2, that is, deg(u)+deg(v)≥n- 1, so there is a Hamilton road in the graph g, so n people can stand in a row, so that everyone in the middle stands on both sides of his friend, and two people at both ends stand next to each other.
D) According to c), any pair of nodes U and V has deg(u)+deg(v)≥n- 1, which proves that when n≥4, there is deg(u)+deg(v)≥n. When U and V are adjacent, there is DEG (U)+DEG (V) ≥