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How to draw the following graph in sagemath?

I am uploading the image here:

https://imgur.com/Q3sUXn8

I know how to draw a graph but I am finding it difficult to draw the graph in exactly the same way as shown in the picture.

Is it possible to do this?

I will be very grateful if someone could kindly help me out

Given a graph $ G$ it is easy to check whether the Graph is planar or not using the command "$G$.is_planar()"

However I am stuck on the following :

Given a non-planar graph $G$ is it possible to find a subgraph of $G$ which is homeomorphic to $K_5$ or $K_{3,3}$?

As per Kuratowski Theorem any Graph $G$ is planar if and only if $G$ has a subgraph homeomorphic to $K_5$ or $K_{3,3}$.

Is it possible to find the required subgraph using sagemath?

Given a matrix $M$ how to form the following matrix $N$ from $M$.

Suppose $M=$\begin{bmatrix} 0 &3 \ 2 &0 \end{bmatrix}

Here $M$ is a $2\times 2$ matrix with 1st row $[0,3]$ and 2nd row $[2,0]$.

We need to form $N$ such that

$N=$ \begin{bmatrix} 3& 3\ 2&2\end{bmatrix}

Here $N$ is a $2\times 2$ matrix with 1st row $[3,3]$ and 2nd row $[2,2]$.

Thus $N$ is formed from $M$ by just adding all the off the diagonal elements of $M$ in a given row to the diagonal element

So the diagonal element of $N$ is the sum of all the remaining entries in a given row of $M$ whereas the rest of the elements of $N$ are the same as $M$.

So the elements of $N$ are obtained from $M$ in the following way :

$a_{11}=0+3=3, a_{12}=3,a_{21}=2,a_{22}=2+0=2$

How to code it?

Please help.

Thank you for your answer

I am extremely thankful for the answer. Can you kindly say how to start learning coding in sagemath? How to know the way to write loops , how to draw a graph, add edges as you have etc.??

I want to write the following code in sagemath but unable to write it:

Suppose we consider the group $\Bbb Z_n$.

We consider an element $a\in \Bbb Z_n$ and form the subgroup generated by $a$ i.e. $\langle a\rangle ={a,2a,3a,\ldots 0}.$

We form a graph $G$ whose vertices are $\langle a\rangle $ and $\langle a\rangle $ and $\langle b\rangle $ are adjacent if either $\langle a\rangle \subset \langle b\rangle $ or $\langle b\rangle \subset \langle a\rangle $ .

How to plot the graph $G$ is Sagemath?

I am giving an example to clear the question:

Consider $\Bbb Z_4$ then consider $\langle 0\rangle $, $ \langle 1\rangle$ , $ \langle 2\rangle$, $ \langle 3\rangle$

Clearly $\langle 0\rangle ={0}$, $ \langle 1\rangle={1,2,3,0}$ , $ \langle 2={2,0}\rangle$, $ \langle 3={0,1,2,3}\rangle$.

Thus the graph $G$ has vertices as $\langle 0\rangle $, $ \langle 1\rangle$ , $ \langle 2\rangle$, $ \langle 3\rangle$ and $\langle 0\rangle $ is adjacent to $ \langle 1\rangle$ , $ \langle 2\rangle$, $ \langle 3\rangle$,

$\langle 1\rangle $ is adjacent to $ \langle 2\rangle$ , $ \langle 0\rangle$,

$\langle 2\rangle $ is adjacent to $ \langle 1\rangle$ , $ \langle 0\rangle$, $ \langle 3\rangle$

and $\langle 3\rangle $ is adjacent to $ \langle 0\rangle$, $ \langle 2\rangle$

Thus $G$ becomes

https://imgur.com/Ef9P4uz

I am extremely thankful for the answer sir. Can you kindly explain the logic behind "if x in d: d[x].append(y) else d[x]=[y]" If you could explain why is it written this way I will be grateful

Okay Thank you so much

How to write the following program in SageMath:

Consider the Permutation Group $S_3$.

The elements of $S_3$ are $e,(12),(13),(23),(123),(132)$.

I want to draw a graph $G$ whose members are the elements of $S_3$ and two vertices $x,y$ are adjacent if and only if $xy\neq yx$.

I am stuck in doing the following things:

1. How to call the elements of $S_3$ through a loop?
2. How to draw the graph $G$ ?

I can check whether they commute or not but I am stuck in the two things. Is there any way to write the code in SageMath?

As an example if I input $S_3$ I want to get the following graph

$G=Graph({1:[2,3,4,5],2:[1,3,4,5],3:[1,2,4,5],4:[1,2,3],5:[1,2,3]})$

Any help will be highly appreciated.

Thanks a lot sir. Can you kindly tell if there is any code which can find all the minimal separating sets of a given graph? How to write such a code

Given a Graph $G$ how can I find the separating set of the Graph?

Suppose I am given this graph G=Graph({1:[2,3,4,5],2:[1,3,4,5],3:[1,2,4,5],4:[1,2,3],5:[1,2,3]})

I want to find the set of vertices whose removal disconnects the graph.

I found that the vertex connectivity of $G$ is 2.

Also on seeing the graph I find that the set of vertices whose removal disconnects the graph will be $(1,2,3)$

But how to find it using a code in SageMath?

Thank you so very much

Consider the Symmetric Group $S_4$

I have three permutations namely $(3,4), (1,2), (1,3)(2,4)$.

How to find the subgroup generated by these permutations ?

Is there any code to calculate in Sagemath the subgroup generated by the permutations given above?

As an example the code should work like this :

If I input $(12)$ the code should give ${(12),e}$

Can someone help please?

I want to input a matrix from a text file and run it in SageMath. The name of the file is Matrix.It is located in the D-drive and it contains a square matrix of order 4.

I changed the the name of the file from Matrix.txt to Matrix.sage. I then wrote load('Matrix.sage');

But I got an error message which read

Traceback (click to the left of this block for traceback) ... IOError: did not find file 'Matrix.sage' to load or attach

Is it possible for Sage-Math to take input a matrix which is stored in a Text File? Can someone kindly comment?

Note:I want to input the matrix from the text file and find its determinant in SageMath.

I am using Sagemath. I have the following query:

I want to find the determinant of a given matrix A. I know it is possible to input the matrix A as A=matrix([[1,3],[3,4]]) and then calculate its determinant as A.determinant()

But I want to calculate determinant of a matrix in the following way:

The matrix A is generated by a C-Program.So I have a C-Program which is Matrix.c and its corresponding output file Matrix.exe. I want to use the matrix A generated from the Program in Sagemath and find its determinant.

Is it possible to input in Sagemath from a output file of a C Program?

I need some help.

I want to solve a matrix equation in SageMath.

I have this matrix

$M=$ \begin{bmatrix}

1&1&1&1&1&1&1

1&-1&1&1&1&0&0\

1&1&-1&1&1&0&0\

1&1&1&-1&1&0&0\

1&1&1&1&-1&0&0\

1&0&0&0&0&-3&1\

1&0&0&0&0&1&-3\

\end{bmatrix}

I have found that det(M)=0 so there exists a non-trivial solution to $MX=0$

I want to solve the equation $MX=0$ but when I solve it in Sagemath I only get the solution $X=0$

How to find non-trivial solution of the system in SageMath??

Please help.

I want to draw a picture of a polygon in SageMath which will be unfilled i.e I want to draw figures of triangle,square,pentagon,hexagon and so on and then draw a figure with say 100 sides.

I checked the web.

I only found plots of 3d figures ,I want 2d figures .

Is it possible to draw such a figure in SageMath.

Please help me

I am new to sage. I have learned the basics of sage programming from various online notes.

I am interested to apply sage in linear algebra and graph theory.

My problem is I want to draw a graph as follows:

Vertices : Subspaces of a vector space of dimension $n$.

Edges: $V_1V_2\iff V_1 \subset V_2$ or $V_2\subset V_1$.

Please don't give me the solution.

Please help me how to write it step by step or give some resources from where I can find this.