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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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Dan Luecking

Posts: 45
Registered: 12/13/04
Re: Is "connected graphs" -> P(trees), G|->{spanning trees of G} one-to-one?
Posted: Mar 4, 2004 12:56 PM
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On Tue, 2 Mar 2004 20:20:59 +0100, "sasha"
<sashaLOESCHEDIESmal.REMOVEITexcite.com@news.sdt.net (AT)> wrote:

>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?


Yes, for simple graphs. No, if loops or parallel edges are allowed:
a graph with one loop and one simple edge has the same spanning tree
as a graph with two edges connecting the same 2 vertices.


Dan

--
Dan Luecking Department of Mathematical Sciences
University of Arkansas Fayetteville, Arkansas 72701
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