Prove that any graph has at least two vertices with the same degree. A complete bipartite graph on ( m , n ) vertices, is a simple graph whose vertices can be divided into two distinct, non-overlapping sets (that is, suppose V has m vertices and W has n vertices) in such a way that there is exactly one edge from each vertex of V to each vertex of W , there is no edge from any one vertex of V to any other vertex of V , and there is no edge from any one vertex of W to any other vertex of W. Use ways to select the edges to show that this graph has m x n edges Use combinations to show that the number of edges on a complete graph is n(n-1)/2