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Some other basic information that should be covered in regard to the fundamentals of graph theory are the ideas of the vertex set and the edge set. While they may be self-explanatory, the vertex set of the graph is a set of all vertices of the graph and an the  edge set is the set of all edges. If we consider the graph pictured above, we define the vertex set as $V=\{1,2,3,4,5,6\}$ and $E=\{\{1,2\},\{2,3\},\{3,4\},\{4,5\},\{1,5\},\{2,5\},\{2,6\},\{5,6\},\{3,6\},\{4,6\}\}$.