The graph below shows 7 vertices (the dots) and 5 edges (the lines)connecting them. An edge here is de ned to be a line that connects 2 verticestogether. In other words, an edge cannot loop back and connect to the samevertex. Edges are allowed to cross each other, but the crossing of 2 edges does notcreate a new vertex. What is the least number of edges that could be added tothe graph, in addition to the 5 already present, so that each of the 7 vertices hasthe same number of edges?Originally Problem 23 from the 2018 Indiana State Math Contest.
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