Is this presentation of cube in plane as a graph wrong?

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My teacher draw cube in graph like this to show us that it is planary my friend says its wrong but I dont get it why , is this really wrong and if yes why ?

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3 Answers

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Your friend is right. Notice that in non-planar cube graph, there are $8$ vertices but in other one, there are more than $8$ vertices. And same argument is valid for edges and faces as well. The planar graph of $3-$cube is generally drew like this:

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This is not correct; graphs must preserve edges, not faces. A cubical graph as below shows the graph is planar.

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What you have drawn is an unfolded cube. You can cut out your illustration and fold it to make a cube. What you are asked to do is to draw a planar graph that reflects the connectivity of the vertices of the cube. There are eight corners, each connected to three others. In your teacher's drawing some of the edges cross, so it does not show the graph can be drawn avoiding that. The assignment is to find a way to draw the graph without any edges crossing. The other answers show how.

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