I am wondering if vertices of a planar graph can lie on top of each other in an embedding of the graph. Also, when drawing a picture/representation of the graph, is drawing vertices on top of vertices precluded?
thanks
2026-03-27 03:41:13.1774582873
In a planar embedding of a graph, can vertices lie on each other?
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No. The definition of a planar graph in Wikipedia does not make it clear, but I'm pretty sure they do not want to allow this. The definition in Wolfram MathWorld does say "no two vertices coincide". And the Wikipedia definition of graph embedding says "no arcs include points associated with other vertices", which at least means that vertices which have any edges must be distinct in the embedding.
Drawing a graph with coinciding vertices is generally confusing, so I don't recommend it.