Symmetry of the cube

Discussion in 'Physics & Math' started by arfa brane, Jan 22, 2019.

1. arfa branecall me arfValued Senior Member

Messages:
7,692
The graph I'm discussing at the moment is any graph, it includes the graph with one vertex and no edges, but don't worry there are plenty more.

3. TheFroggerBannedValued Senior Member

Messages:
2,175
I see now! Okay. A graph with one vertex? How would that work? Space is in more than one-dimension.

5. TheFroggerBannedValued Senior Member

Messages:
2,175
Hi again.

The only way I can envisage a graph with one-vertices is if it's a circle.

7. arfa branecall me arfValued Senior Member

Messages:
7,692
Sure, a graph is a topological object with vertices and edges, it doesn't care about how many dimensions there are.

The graph of one vertex can have edges, but you need to decide if it's ok to just add edges to a graph.

The context is that you can 'walk' through a graph from point to point along edges. A graph with one point (vertex), can only have edges from the single point to itself. The edges are loops; any single point with looped edges (assuming you can add loops to a point freely) has a graph-walk that goes from the point to the point, so you're left with counting how many times you do this. Also, because you move from point to point a direction (at least along each edge in the graph-walk) is defined.

But counting edges (or walking between points) is equivalent to labeling edges with numbers; if you count the points you pass through though, you get 1 in a 1-vertex graph with multiple loops. Drawing a loop not on a vertex isn't allowed--you would have a free loop.

Last edited: Jan 28, 2019
8. arfa branecall me arfValued Senior Member

Messages:
7,692
Yeah, interesting since I'm talking about loops, but as edges. Maybe you can transform an edge into a vertex or something?

So more formally, a 1-vertex graph is an order 1 graph, and any looped edges are 1-cycles.
In this graph, "counting" can be defined if for instance you decide to count to n, by adding n loops to the vertex (so you can walk along n edges).

Last edited: Jan 28, 2019
9. arfa branecall me arfValued Senior Member

Messages:
7,692
A graph is disconnected if there are no edges between vertices. So a 1-vertex graph even with looped edges is disconnected.
This makes sense because a disconnected graph of order n can have loops in it too, and the structure (there isn't much of it) isn't changed.

A complete graph is a vertex set with every vertex adjacent to every other vertices; i.e. to n-1 vertices.

10. TheFroggerBannedValued Senior Member

Messages:
2,175
What about the value of, "z": the height on a graph of x,y and z?

11. arfa branecall me arfValued Senior Member

Messages:
7,692
"Height" still isn't defined, nor is "width". Not even "length". Only "adjacent" has been defined, apart from walking through a graph, or traversing it. Doing a traversal means there is a direction, but so far, only along an edge.

12. arfa branecall me arfValued Senior Member

Messages:
7,692
--https://en.wikipedia.org/wiki/Graph_product

13. someguy1Registered Senior Member

Messages:
727
I surely said no such thing. I said that two particular groups were isomorphic. You keep claiming without explanation that some graph can be associated with some group, but you never say how. It makes me think you know a lot of buzzwords but lack the mathematical experience to put them into context. You misuse and misunderstand virtually every technical term you drop into the conversation.

Anyway just dropped in for a moment and you didn't disappoint. You should try some self awareness.

Last edited: Jan 29, 2019
14. arfa branecall me arfValued Senior Member

Messages:
7,692
This from someone who has misunderstood almost everything I've posted and seems to be looking for anything they can complain about.

You seem to have zero understanding of what the graph of a group is. Everything you've had to say so far has been almost completely irrelevant. I mention a hexagonal graph, you think I'm talking about the symmetry group of a fucking hexagon! Ridiculous.
You change the subject and accuse me of changing the subject and avoiding your questions. What fucking questions? Your posts are fucking irrelevant to this thread. Grow the fuck up.

If you still don't get it, it goes like this: I don't give a flying fuck about your objections, none of them make much sense to me (although I understand the mathematical context you put them in, I don't understand why you're doing it or what it has to do with me), although I suspect you feel they're just wonderful. You lack the experience to put anything about graphs (very simple objects) into any context. Maybe you don't know what a context is?

I think the best thing I can do about you is ignore you, you don't seem to have anything to say. Why not just fuck off?

Last edited: Jan 29, 2019
15. arfa branecall me arfValued Senior Member

Messages:
7,692
See, that right there tells me you aren't looking at the topic, you're looking at ways to make me look stupid.
But your post is facile, a ridiculous thing to say. Except for the first sentence, which is the only accurate one.

When I first read it, alth0ugh it wasn't the first post of y0urs in this thread with the same tone, I really had to think about where you could possibly have got the idea I said there's more than one cyclic group isomorphic to a group of order 6, when I've been talking about graphing the symmetries of such groups, and other groups, not isomorphic to an order 6 group.

Which seems to have whooshed straight over your silly head. You aren't on-topic here, maybe you think you've been digging a hole for me. I think you fell in to the hole some time ago, possibly before you read my OP.

Last edited: Jan 29, 2019
TheFrogger likes this.
16. TheFroggerBannedValued Senior Member

Messages:
2,175
Arfabrane, a graph has three dimensions: x,y and z PLUS the value stored at that location. This gives four digits in total.

17. arfa branecall me arfValued Senior Member

Messages:
7,692
What if the graph has no values at any location, it's a bare graph with vertices and edges and nothing else?

What if the graph is one of these?

What if you figure out after a bit of thinking, that some of the above can be drawn on a sphere without intersections?

18. TheFroggerBannedValued Senior Member

Messages:
2,175
You still should have values stored AT those locations. This is the essence of computing: you have a location in memory with a value stored AT that location.

Messages:
7,692
20. arfa branecall me arfValued Senior Member

Messages:
7,692
Yeah, but unfortunately it isn't the essence of graph theory. The theory is about connections between vertices, how many ways there are to get from one vertex to another vertex, lots of other things too, all based on connectivity.

For instance there are five distinct kinds (data types ?) of connections between any two vertices:

A walk; a trail; a path; a circuit; a cycle.

21. TheFroggerBannedValued Senior Member

Messages:
2,175
What if the value stored at each location of the graph was that position's location in time?

Last edited: Jan 30, 2019
22. arfa branecall me arfValued Senior Member

Messages:
7,692
Can you explain to me where this value came from, and what do you mean by "position" and "time"?
If you're talking about geometry, I've explained it already--there isn't any geometry unless you impose it.

23. TheFroggerBannedValued Senior Member

Messages:
2,175
Hi there.

You have your, "single-vertice", and points plotted from this (step 0.25,-10, 25.) At each point, a value can be stored which locates the position in time.

You could also locate your single axis from the points:!,@,#,\$,%,^,&,*,(,).