1. The problem statement, all variables and given/known data Hello everyone; This is the problem that I am working on: (a) - Show that in every graph there are two vertices of the same degree. (b) - Determine all graphs with exactly one pair of vertices of equal degree. 2. Relevant equations None. 3. The attempt at a solution For part (a) I assumed a graph of order n with the largest possible degree is (n – 1), and the smallest possible degree is zero. Next, I showed that if every vertex in this graph has a different degree than the others, then the vertex with degree (n – 1) will have to be connected to the vertex with degree zero, which is a contradiction. Part (b) is where I’m stuck; I’ve been looking at graphs with 2, 3, and 4 vertices to see if I can get a certain pattern but I can’t seem to find it. So any help would be appreciated; thanks in advance.