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A graph is called planar if it can be drawn in the plane without any edges...

A graph is called planar if it can be drawn in the plane without any edges crossing. The Euler’s formula states that ve + r = 2, where v,e, and r are the numbers of vertices, edges, and regions in a planar graph, respectively. For the following problems, let G be a planar simple graph with 8 vertices.

  1. Find the maximum number of edges in G.
  2. Find the maximum number of edges in G, if G has no circuits of length 3.

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