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The edge connectivity of a connected graph G  is the minimum number of edges whose deletion from the graph G disconnects G. Below we are concerned with a particular kind of edge-cut.

• For a connected graph G=(V ,E), an edge set S ⊂ E is a restricted-edge-cut, if G−S is disconnected and every connected component of  G−S has at least 2 vertices. 

Clearly, a restricted-edge-cut is an edge cut with a special requirement.

• The restricted-edge-connectivity of G, denoted by κres(G), is defined as the cardinality of a minimum restricted-edge-cut.

For example, a graph g is as follows.

Clearly, its edge-connectivity is 1 since (0,3) or (0,4) is a edge cut of g. But we can find that  if we remove the edge (0,3), then "3" is a isolated vertex. Similarly, "4" is a isolated vertex if we remove  (0,4). It is not difficult to find g has exactly the two cut-edges (0,3) and (0,4).

Based on the definition of the restricted-edge-cuts, neither {(0,3)} nor  {(0,4)} are restricted-edge-cuts.  A minimum restricted-edge-cut is {(0,1),(0,2)} since every connected component of G-{(0,1),(0,2)} has  (at least) 2 vertices.

So  κres(g) is 2.  My problem is:

Given a graph G, how to calculate the restricted-edge-connectivity of  G?  Moreover, how to find a minimum restricted-edge-cut? 

A specific graph that I want to test is as follows. (it has 16 vertices and 56 edges.) I would like to calculate its restricted-edge-connectivity and find a minimum restricted-edge-cut. 

g:=ConvertGraph("O~tIID@wL~j`PbOqgLJ@p");
DrawGraph(g, stylesheet=[vertexborder=false,vertexpadding=15,edgecolor = "Black",
     vertexcolor="Black",edgethickness=2])

EdgeConnectivity(g) 

6

One option I came up with is to find all 6-edge subsets first. Test if they satisfy  the restricted condition (one by one). Then continue to increase to 7 or more. But this violent calculation may get stuck in the first step. That is, test all the minimum edge cut sets (Note that we will consider 32468436 edge-subsets!) I was referring to the efficiency aspect.  

with(Iterator):
C:=Combination(58,6):
K:=Edges(g):
#sub:=seq( K[[seq(c[]+1)]], c=C); # do not run this code since it has 32468436 members.

Any language is acceptable.( C or C++, Python. )

PS: Some time ago, I also asked a related question (but with some differences) on mathematica stack （Find all the minimum edge cuts of a graph）. Although Bob Hanlon  gave a reply, the actual result is not good.

Edits: The following literature gives a polynomial algorithm for computing the restricted-edge-connectivity of a given  graph. The heart of it is to computing the least cardinality of some  edge-pairs's edge separator. I'm stuck here.

• Esfahanian A H, Hakimi S L. On computing a conditional edge-connectivity of a graph[J]. Information processing letters, 1988, 27(4): 195-199.

How to implement this algorithm is my current concern.

Hello:

I've changed my laptop this week and I'd like to know how to install Maple with my account in the new one.

Thanks in advance.

Sergio Sanz.

 Help in writing Maple code to transform differential equation with partial derivatives into ordinary differential equation

Hello everyone!

Please help me with this issue.
I have a plot with three curves and when I do any modification to the view (zoom in/out, pan) one of those curves disappears.

This is the plot before the modification of the view:


And this is the plot after the modification: (I just selected the "pan" option and clicked the plot)


What can I do to keep in view all the curves?
Thanks.

SDFS_primer_intento.mw

How do i solve nonlinear coupled orinary differential equation with boundary conditions?

Please how  can I use getdata to extract only 200x2 of 208x2 matrix from maple to excel.

For instance I have:

Q:= ( seq( seq( plottools:-getdata(ans1[s1,3])[j,3],j=1..3), s1=1));

It returns  208x2,  200x2 200x2 matrices and I can't extract it using 

`<|>`( seq( seq( plottools:-getdata(ans1[s1,3])[j,3],j=1..3), s1=1));

because the matrices have different dimension. Please, how can make 208x2 matrix to 200x2?

After I refer to the Mersenne prime number table, I found the following result
5, 31, the number of digits is too large to be determined
13, 8191
17, 131071
19, 524287
If the following elements all yield composite numbers
So:
2, 3, 7, 127
The length of the sequence with only 2 only generators reaches 4.
Due to its particularity, it is guessed whether 2^(2^127-1)-1 is also a prime number,
and whether the sequence with 2 as the generator is an infinite sequence of prime numbers Woolen cloth? 
Then perfect numbers are also infinite.

I have created some plots of inverse primes  like this example1.pdf .

The filled color-shape in the middle is what I want do do with all areas in this picture or in other pictures.

In other words the goal is to fill the differnt areas in the print with different colors.

So I need to find the points of the Polygons, as I have done by hand with that yellow Polygon.

A procdure that is ready will give give the crosspoints of the lines.

These are the line-coordinates (the 1st number ist the number of iterations)

2*L[1]=number of lines in L

L:=[14, [[1, 1], [1, 26]], [[1, 26], [26, 26]], [[26, 26], [26, 37]], [[26, 37], [37, 37]], [[37, 37], [37, 39]], [[37, 39], [39, 39]], [[39, 39], [39, 20]], [[39, 20], [20, 20]], [[20, 20], [20, 23]], [[20, 23], [23, 23]], [[23, 23], [23, 30]], [[23, 30], [30, 30]], [[30, 30], [30, 70]], [[30, 70], [70, 70]], [[70, 70], [70, 45]], [[70, 45], [45, 45]], [[45, 45], [45, 34]], [[45, 34], [34, 34]], [[34, 34], [34, 32]], [[34, 32], [32, 32]], [[32, 32], [32, 51]], [[32, 51], [51, 51]], [[51, 51], [51, 48]], [[51, 48], [48, 48]], [[48, 48], [48, 41]], [[48, 41], [41, 41]], [[41, 41], [41, 1]], [[41, 1], [1, 1]]]

These are the crosspoints:

cp := [[23, 26], [30, 37], [32, 37], [26, 30], [48, 45], [39, 34], [41, 34], [45, 41]]

To plot the pdf I used this code:

poly2 := [[32, 32], [34, 32], [34, 34], [39, 34], [39, 39], [37, 39], [37, 37], [32, 37]]

poly 2 is just an axample, how it looks like when its ready.

display(seq(line(op(L[i])), i = 2 .. 2*L[1] + 1), polygonplot([poly2], color = "Resene GoldenTainoi", axes = none, style = polygon), color = blue, thickness = 0.8);

So I hope, you can help me :)

This is a beautyfull way to paint a prime  by just printing the remainders of the recursive dividing of the inverse prime in lines.

Thanks a lot,

Arno

For example my friend emailed me.

His email address is oneman@gmail.com, the email content is HELLO.

How does Maple print HELLO to the screen so I can see it?

Thanks for your help!

I make new cone puzzle. However, I cat't make function l(θ). Can maple solve this puzzle?

θ=90 degree is a YouTube problem I found. 

Good day.

Several years ago, I obtained access to a clustering package that was useful to my studies using Maple 17.

In the meantime, I switched to another computer and now, I  cannot access the file, ClusterAnalysis.mla.

Unfortunately, I do not recall how I was able to access this library file.

Can anybody please advise me on the exact steps that are necessary to initialize and execute this file?

Thanks for reading ...

Please help me create a variation table of the function in maple like the above figure.

I haven't managed to round values with units, and get the trailing zeroes cut away, so I'd like to use the MapleTA:-Builtin:-numfmt function to do the job.

The problem is, that this function doesn't accept values with units.

I have managed to write a rounding function to do the rounding, but the problem here is that it will write the values with trailing zeroes, which isn't what I want.

Any ideas how to fix that?

I want to change the colors of a contour such that the region above zero is represented by a different color instead of yellow color,  and that the colors for conts <0 are one set of colors (maybe yellow to red), and the area for which conts >0 is one color which is very different from the others (so maybe white).

Case4Contour.mw