I was wondering if someone can help me understand how prove that this graph is connected.
Given a graph with n vertices, prove that if the degree of each vertex is at least $(n − 1)/2$ then the graph is connected.
So far I know that about connected graphs:
An undirected graph is called connected if there is a path between every pair of distinct vertices of the graph
The distance between two vertices in a graph is the length of the shortest path between them.
The diameter of a graph is the distance between the two vertices that are farthest apart.