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if we have a relation like this : $(x_1,\ldots,x_n)$ is related to $(y_1,\ldots,y_n)$ iff

$$x_i-y_i= x_{i-1} * y_1 \qquad \mbox{for } i\gt 1 $$

the $x_i$s and $y_i$s are elements of a field $\mathbb{F}_q$.

and two points are connected if they have this relation..

Any ideas about how I can generate such a graph ?

edited Nov 1 2011 at 0:36

David Roberts
11.7k●2●18●55

asked Nov 1 2011 at 0:27

Hilbert
1

1

I'm afraid I don't understand what you are asking for. What do you mean by "generate"? Do you want a description? an algorithm? a picture? – Yemon Choi Nov 1 2011 at 0:32

In what context did this question arise? What do you already know about the problem? Please see the FAQ for reasons why this might be closed mathoverflow.net/faq#whatquestions. In the event that this question is closed, please consider asking it at one of the other Q&A sites also listed in the FAQ. – David Roberts Nov 1 2011 at 0:33

I've edited to include LaTeX. – David Roberts Nov 1 2011 at 0:36

Best to start with $n=2$. Then it looks like $x_2-y_2=x_1 * y_1$, a fairly simple graph. More generally, if you're interested in the visual aspect, a simple linear change of variables gives $y_i=x_{i-1} * y-1$. It should be pretty clear what that looks like. – Will Sawin Nov 1 2011 at 4:54

Thanks for your comments. Actually, this is a special type of graphs called Wenger's graph, the thing is I have no idea about programing and computing. and i need to try to have the graph ( using maple or mathematica) but i don't know how I can represent the edge between two vertices (x_1,....,x_n) and (y_1,....,y_n). these two vertices are adjacent if they satisfy y_i - x_i = y_1 x_(i-1). – Hilbert Nov 1 2011 at 14:03

how can I draw a graph if I know the vertices and the edges between two vertices (x_1,…,x_n) and (y_1,…,y_n) is given by a system of equation ?

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