For one of my homework assignments I'm being asked to list all the possible plane graphs with four vertices but surely there would be an infinite number of those? Nowhere in the question does it say that the graphs must be simple. Is this an error in my understanding of plane graphs or an error in the question?
2026-03-27 17:36:03.1774632963
Problem with planar connected graphs
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I think that the question assumes that the graphs are simple. Otherwise yes, there are an infinite number of non-simple planar graphs on four vertices (you just have to keep adding multiple edges).
It depends on the context of the homework question (From a textbook or a professor? In a CS class or a Mathematics class?), but I find that most of the time when talking about graphs, the graphs are assumed to be simple unless stated otherwise.