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Thu 29 Sep, 2005 12:22 am
Hi all! Does there exist a graph such that it has ONE and only ONE Euler Circuit? In other words, a graph which is Eulerian but not Randomly Traceable. Thanks!
I think
I think NO
Because a euler circuit can start and end ONLY at the ODD degree vertices of a graph. So for a gragh to have only ONE Euler ciruit there has to be ONLY one ODD degree vertex in the graph.
IT IS NOT POSSIBLE TO HAVE A GRAPH WITH ONLY ONE ADD DEGREE VERTEX
You can try one.
Re: I think
vinsan wrote:I think NO
Because a euler circuit can start and end ONLY at the ODD degree vertices of a graph. So for a gragh to have only ONE Euler ciruit there has to be ONLY one ODD degree vertex in the graph.
IT IS NOT POSSIBLE TO HAVE A GRAPH WITH ONLY ONE ADD DEGREE VERTEX
You can try one.
I thought Eulerian graphs were only allowed to have even degree vertices.
Re: I think
vinsan wrote:I think NO
Because a euler circuit can start and end ONLY at the ODD degree vertices of a graph. So for a gragh to have only ONE Euler ciruit there has to be ONLY one ODD degree vertex in the graph.
IT IS NOT POSSIBLE TO HAVE A GRAPH WITH ONLY ONE ADD DEGREE VERTEX
You can try one.
I thought Eulerian graphs were only allowed to have even degree vertices.
Re: I think
vinsan wrote:I think NO
Because a euler circuit can start and end ONLY at the ODD degree vertices of a graph. So for a gragh to have only ONE Euler ciruit there has to be ONLY one ODD degree vertex in the graph.
IT IS NOT POSSIBLE TO HAVE A GRAPH WITH ONLY ONE ADD DEGREE VERTEX
You can try one.
I thought Eulerian graphs were only allowed to have even degree vertices.
Its like...
I never said Eulerian graphs aren't allowed to have even degree vertices.
I feel that exactly one euler circuit (start and edn on same vertext) can exist there has to be ONLY one ODD degree vertex in the graph i.e if the graph has N vertices out of which N-1 are even and 1 is ODD ---------- SUCH GRAPH NOT POSSIBLE.
So ONLY one Euler circuit is not possible.
A point with one line as a loop starting and ending on it fit the need?
Quote:A point with one line as a loop starting and ending on it fit the need?
Wouldn't that be possible only in a non-ecleadian space?
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