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 ...
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 ...
| № | Пользователь | Рейтинг |
|---|---|---|
| 1 | Benq | 3676 |
| 2 | Kevin114514 | 3659 |
| 3 | jiangly | 3640 |
| 4 | turmax | 3450 |
| 5 | tourist | 3408 |
| 6 | strapple | 3360 |
| 7 | Um_nik | 3354 |
| 8 | squareOf105 | 3348 |
| 9 | maroonrk | 3312 |
| 10 | idontwannadothis…e | 3191 |
| Страны | Города | Организации | Всё → |
| № | Пользователь | Вклад |
|---|---|---|
| 1 | Qingyu | 155 |
| 2 | nik_exists | 151 |
| 3 | maspy | 149 |
| 4 | AmShZ | 145 |
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| 6 | Errichto | 139 |
| 7 | BledDest | 136 |
| 8 | adamant | 135 |
| 9 | maroonrk | 132 |
| 10 | cry | 130 |
Obviously no, check this one : 1-2-3-4
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 ...
"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.
a tree either has a single centroid or two neighbouring centroids.
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!