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ChemliYoussef's blog

centroid of a tree
By ChemliYoussef, history, 10 years ago, In English

hello everyone , I want to know if a tree has a single centroid because I encounter some cases where I find 2 centroids...
thanks in advance ...

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10 years ago, hide # |
 
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Obviously no, check this one : 1-2-3-4

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    10 years ago, hide # ^ |
     
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    The reason of my question was being confused by jordan 1869 theorem : " there exists a vertex whose removal partitions the tree into components, each with at most N/2 nodes. " I didn't know if it is talking about only one vertex or more ... thanks a lot ...

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      10 years ago, hide # ^ |
       
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      "There exists" means that there is at least one, but there could me multiple ones.

      Actually, there can be at most 2 centroids in a tree and this happens when there's an edge whose deletion splits the tree in half.

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10 years ago, hide # |
 
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a tree either has a single centroid or two neighbouring centroids.

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10 years ago, hide # |
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If your question is that is there any tree with one centriod:

yes a star( V=1..n , E=(1,n),(2,n)...(n-1,n) ).

else

tree has at most 2 centroids that if they are 2 they are connected!

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