## GraphTheory: creating a minimum spanning tree star...

Suppose,  there are

• 50 vertices

• list of coordinates of these 50 vertices

Now I want to create a graph with minimum distance.

The starting point of the graph should be vertice 1. From there,  the closest point has to be added to a list X. and from this point, it should calculate again the closest point and add this value to the same list X.

So actually I want to start in point 1 and I want to see the sequence of how the graph (I think minimum spanning tree?) is created

How can I code this in Maple?

## How do I generate all non-isomorphic trees of orde...

I could keep on using the commands

with(GraphTheory):

with(RandomGraphs):

DrawGraph(RandomTree(7))

but then this is not helpful because I do not get non-isomorphic graph each time and there are repetitions. So any other suggestions would be very helpful.

## How to color a copy of a Graph without altering th...

Hi,

This question concerns the package GraphTheory
( Maple 2015 on a Windows 7 PC )

Let G1 be some graph and V a list of vertices in G1
The default colors DrawGraph uses for the vertices is yellow

I define the graph G2 this way :
G2 := copy(G1):
HighlightVertex(G2, V, red);
DrawGraph(G2);
Obviously the result is a graph where vertices in V are red while the remaining ones are still yellow

Question 1 :  Why does the command DrawGraph(G1) returns exactly the same picture ?
I have thought that defining G2 as a copy of G1 would have preserved the default colouring of the vertices.
Note that the same undesired (at least for me) thing occurs with the  HighlightEdges command.

Question 2 : Is it possible to retrieve the original colouring of G1 without using HighlightVertex(G1, V, yellow)  ?

## Is it possible to give an edge of a graph an infin...

Hi everybody,

Only weights of type "numeric" can be used in a weighted graph (package GraphTheory) .
Is it possible to bypass this limitation and affect an infinite weight to an edge ?
If not possible, does it exist some "highest numeric value" in Maple I could use instead ?
(the trick of a very high value doesn't suit me)

Subsidiary question : is it possible to change the printing format for those weights ?
For instance   GraphTheory:-SetEdgeWeight(MyGraph, MyEdge, 123.4) plots the value 123 on edfe MyEdge

## Vertex Weight graph theory...

how to define VertexWeight in Graph Theory package

## Search for an explanation about CycleBasis...

Could someone please explain to me why the procedure GraphTheory:-CycleBasis requires that the vertices of a graph be integers for it to work correctly ?
(while the definition of a graph supports other types of vertex names)

restart:
with(GraphTheory):

#------------------------------------------------------- test 1

g1 := Graph({{"a", 1}, {1, 3}, {"a", 3}});
DrawGraph(g1);
CycleBasis(g1);

Error, (in GraphTheory:-CycleBasis) cannot determine if this expression is true or false: "a" < 1

#------------------------------------------------------- test 2

g2 := Graph({{a, 1}, {1, 3}, {a, 3}});
CycleBasis(g2);

Error, (in GraphTheory:-CycleBasis) cannot determine if this expression is true or false: a < 1

#------------------------------------------------------- test 3

g3 := Graph({{4, 1}, {1, 3}, {4, 3}});
CycleBasis(g3);

[[1, 3, 4]]

Knowing this limitation I usually rename to integers the vertices of the graphs, next do some operations, and next go back to the original names.

Thanks for any explanation.

## How to simulate random walks on graphs?...

This week I am participating in 19th Ising lectures (see https://drive.google.com/folderview?id=0B0uPwoK-03XgSEZpYWljYnpXN0U&usp=sharing). The Serguei Nechaev's talk inspired me to ask the question:
"How to simulate a random walk on an undirected and unweighted (and, of course, connected) graph
(All the paths from a vertex of degree k have the same probability 1/k.)?"
A Maple procedure to this end is welcome.

## Approximate solution of Traveling Salesman Problem...

I am looking for a quick implementation in Maple to approximate a solution to the travelling salesman problem in a graph of several thousand vertices randomly placed in the unit square. I've tried TravelingSaleman in the GraphTheory package; it bogs down with just a handful (say, twelve) of vertices. I also tried Bruno Buerrier's implementation of the two-opt algorithm; on my machine that took more than a day for 2048 vertices.

Is anyone aware of a quicker implementation in Maple?

## Konigsberg Graph?...

Hello I'm having trouble create Konigsberg Graph on Maple. Here's the picture. Sorry if it's not clear enough. Thanks!

## Novice Attempt in Graph Theory...

I do not know! I am a novice in maple as well as in graph theory. I attach a doc in which i attempted to learn what is network. It seems alright with maple as it gives as what it understands as horizontal and vertical network. I do not expect a horizontal line as horizontal network and vertical line as vertical network, in which case a horizontal line with nodes 1 and 2 will be vertical network if  draw it vertically. The maple, in my opinion ( i am not a maple man) gives the answer in a vertical pattern, rightly so for clarity and space constraint.

I am sorry if i am confusing.  The document in my attempt to know more may give you also more insight. Thanks.

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## DrawNetwork horizontal option...

In Maple 2015, the DrawNetwork command option "horizontal" does not seem to work. Is this a bug? It doesn't even display horizontally on the online Maple Help webpage. Any help would be appreciated.

In the below file, I have tried to create tree using Graphtheory and export it to file. But exporting works only if I read the procedure twice and that too after running the procedure.

test.mw

testproc.txt

## How to make box shaped nodes to circle shaped in G...

I found some codes for drawing my Graph in Maple:

[>  with(GraphTheory);

W := Graph(undirected, {{0, 1}, {0, 2}, {0, 3}}):

HighlightEdges(W, W, black):

HighlightVertex(W, [1, 2, 3, 0], gray):

DrawGraph( W);

The way that the graph was plotted was not what I wanted to have. In fact, I expected to have something like this one:

http://i.stack.imgur.com/JMfmd.png

I mean the vertexes are shaped by circles not by boxs. Moreover, one may want to see labels below (or above) the circled nodes. My question is

" Is there any certain codes we can use to have this graph like the picture above? Can we manage the labels to be appeared near the nodes in Maple?