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Are all maximal subtrees of a simple connected graph isomorphic? any hints?

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up vote 3 down vote accepted

The answer is a resounding "No". Even as small as the complete graph on four vertices, one can find nonisomorphic spanning trees.

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The number of nonisomorphic trees grows reasonably quickly after that. For example, the complete graph on ten vertices has 106 nonisomorphic spanning trees.

(Incidentally, here is a small collection of spanning trees you might find interesting.)

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Thanks, a lot, for the link too, it seems interesting. I will have a look –  StudentMath Oct 11 '12 at 0:02

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