A complete graph is a graph where every vertex is adjacent to every other vertex. In 1889

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A complete graph is a graph where every vertex is adjacent to every other vertex. In 1889 Arthur Cayley proved that a complete graph with n vertices has nn-2 spanning trees.

a. How many spanning trees are there for a complete graph with 3 vertices, according to Cayley’s theorem? Verify this number by drawing a complete graph with 3 vertices and then finding all the spanning trees.

b. How many spanning trees are there for a complete graph with 4 vertices, according to Cayley’s theorem? Verify this number by drawing a complete graph with 4 vertices and then finding all the spanning trees.

c. How many spanning trees are there for a complete graph with 5 vertices?

d. How many spanning trees are there for a complete graph with 6 vertices?

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