(a) Does there exist a connected planar graph with 100 vertices and 300 edges? (b) Does...

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(a) Does there exist a connected planar graph with 100 vertices and 300 edges? (b) Does there exist a connected nonplanar graph with 555 vertices, 558 edges and minimum degree at least two? Justify your answers by either constructing such a graph or by showing no such graph can exist. Note that Question 2 on this assignment is worth 10 points instead of the usual 5. (a) Does there exist a connected planar graph with 100 vertices and 300 edges? (b) Does there exist a connected nonplanar graph with 555 vertices, 558 edges and minimum degree at least two? Justify your answers by either constructing such a graph or by showing no such graph can exist. Note that Question 2 on this assignment is worth 10 points instead of the usual 5.