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Topic: Is "connected graphs" -> P(trees), G|->{spanning trees of G} one-to-one?
Replies: 6   Last Post: Mar 15, 2004 11:00 AM

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sasha

Posts: 2
Registered: 12/13/04
Is "connected graphs" -> P(trees), G|->{spanning trees of G} one-to-one?
Posted: Mar 2, 2004 2:20 PM
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Hello everyone!

For a given natural number m, is the map

connected graphs with m edges -> power set of trees,
G |-> {spanning trees of G}

one-to-one?

And the more general map
connected graphs-> power set of trees,
G |-> {spanning trees of G}?

For simplicity, we assume that the nodes are always the first n natural
numbers, for a convenient n.
And how about graphs up to isomorphy?

best regards,
Sasha.






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