A connected graph has nine vertices and twelve edges. Does it have a circuit? Why or Why not?

a:The graph has a circuit because every graph with an odd number of vertices and an even number of edges has a circuit.

b:The graph has a circuit because a connected graph with no circuits would be a tree, and a tree with nine vertices would have eight edges, not twelve.

c:The graph does not have a circuit because any connected graph with nine vertices has eight edges, not twelve, and therefore cannot have a circuit.

d:The graph does not have a circuit because no graph with an odd number of vertices and an even number of edges has a circuit.