How many vertices and edges does the complete tripartite

Question

Question: 1. The complete bipartite graph Km,n ...

(a) . . . has m+n vertices. Prove it.

(b) . . . has m · n edges. Prove it.

2. How many vertices and edges does the complete tripartite graph K_m,n,p have? Prove your conjecture.

3. To what graph is K₅ \ K₃ isomorphic? How about K₆ \ K₃? (Any conjectures?)

4. The star graph on n vertices has one vertex adjacent to all other vertices (and no other adjacencies). Conjecture and prove a formula for the number of edges of the star graph on n vertices.