A graph that is both bipartite and complete is:A. PlanarB. TreeC. CycleD. Complete bipartite graph

To answer the question regarding a graph that is both bipartite and complete, let's analyze the provided options:

1. Definition Context

• Bipartite Graph: A graph that can be divided into two distinct sets, such that no two graph vertices within the same set are adjacent.
• Complete Graph: A graph in which every pair of distinct vertices is connected by a unique edge.
• Complete Bipartite Graph: A special type of bipartite graph where each vertex of one set is connected to every vertex of the other set.

2. Evaluation of Options

1. A. Planar - While bipartite graphs can be planar, not all complete graphs (especially when there are many vertices) are planar.
2. B. Tree - Trees are a type of graph that is bipartite; however, they are not complete as not all possible edges exist.
3. C. Cycle - Cycles can be bipartite if they are even, but they are not complete unless they consist of only two vertices.
4. D. Complete bipartite graph - This directly matches the criteria since it is defined as a graph that is both complete and bipartite.

3. Conclusion

Given the definitions and evaluation of the options, the answer is clear.

Final Answer

D. Complete bipartite graph