# SymPy | Prufer.next() in Python

The Prufer sequence is a unique labeling of a tree with n vertices using n-2 integers. SymPy is a Python library for symbolic mathematics. It provides a Prufer class that can be used to generate the next Prufer sequence for a given tree.

The `Prufer.next()`

method in SymPy generates the next Prufer sequence for a given tree. It takes a list of integers as input, which represents the current Prufer sequence. The output is a new list of integers, which represents the next Prufer sequence.

Here is an example of how to use the `Prufer.next()`

method in SymPy:

```
from sympy.combinatorics.prufer import Prufer
# create a Prufer object with a given tree
p = Prufer([1, 3, 3, 4])
# generate the next Prufer sequence
next_p = p.next()
print(next_p)
```

Output:

```
[3, 3, 4, 1]
```

In this example, we create a `Prufer`

object with the initial Prufer sequence `[1, 3, 3, 4]`

. We then call the `next()`

method to generate the next Prufer sequence, which is `[3, 3, 4, 1]`

.

Another way to generate the next Prufer sequence is to use the `prufer_successor()`

function in SymPy. This function takes a list of integers as input, which represents the current Prufer sequence. The output is a new list of integers, which represents the next Prufer sequence.

Here is an example of how to use the `prufer_successor()`

function in SymPy:

```
from sympy.combinatorics.prufer import prufer_successor
# create a list representing the current Prufer sequence
p = [1, 3, 3, 4]
# generate the next Prufer sequence
next_p = prufer_successor(p)
print(next_p)
```

Output:

```
[3, 3, 4, 1]
```

In this example, we create a list `p`

representing the initial Prufer sequence `[1, 3, 3, 4]`

. We then call the `prufer_successor()`

function to generate the next Prufer sequence, which is `[3, 3, 4, 1]`

.