Discussion
Two graphs A and B are shown below : Which one of the following statement is true ?
Answer: A
Graph A is the complete graph on four vertices, drawn with its two diagonals crossing. It is planar, since one diagonal can be drawn outside the square without crossing the other edges. Graph B is the cube, which is also planar: drawn with one square inside the other and the corners joined, no edges cross. So both A and B are planar. The statements that neither is planar, or that only one is, are wrong. The graphs that cannot be drawn without crossings are those containing \(K_5\) or \(K_{3,3}\), which neither A nor B does. The keyed answer is the first option.
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