# Number of edges in low complexity graphs

Is the number of edges in the 3-connected graph with the minimum number of spanning trees always $\lceil {\frac{3}{2}}n\rceil$?

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What are some examples of such 3c-min-span graphs? Presumably you know some classes that achieve the min... – Joseph O'Rourke Oct 14 '10 at 19:40
It seems there are no classes which achieve the minimum always. An example of a class which achieve a low number of spanning trees are Prism Graphs, but they do not always have the minimum number of spanning trees. – utdiscant Oct 14 '10 at 20:50
For what values of n do you know this to be true? – j.c. Oct 15 '10 at 0:18