# In search of a symmetric homogeneous graph with a pivotal origin

I'm trying to design a computer game and I need a symmetric homogeneous graph with a pivotal origin which will act as the map of the game (players will walk according to it).

Here's an example of what I'm looking for:

Let me describe this game:

1. Players can walk on the edges landing on vertices.
2. Blue dot marks the final destination.
3. Yellow dots show stages one prior to final one and they are all of the same value (difficulty level). This goes on as we get farther from the center. In other words the difficulty level drops by the number of edges remaining to the pivot.
4. The purpose of the game is to players fight their path through for the blue dot.

What are desired characteristics of this pattern:

1. It has a central point which can be considered as the final stage.
2. Number of vertices of the same value grows as we get farther from the origin.
3. All the vertices have the same number of neighbors (6, event though the number 6 itself is not important but to keep the game simple, the lower the better).

As perfect as this graph is, it still has got one problem. It's not completely fair. Take vertices 1 and 2 for example. Player 1 has only one path to next level while player two has 2 (one adjacent yellow dot by P1 and two adjacent yellow dots by P2).

Does anyone know of a similar pattern which is also fair?

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Is this a visual pattern you're looking for or a usage pattern? –  Robert Koritnik Sep 26 at 8:21
Are they any different? You can always use a visual pattern for other purposes! It's an idea that I'm looking for. –  Mehran Sep 26 at 8:30
If its' not about a visual pattern specifically I think you've posted to an out-of-your-question-scope Q&A site. This one's about graphic design specifically. And not usability. That's a different site. And no visual is not the same as math graphs... I suggest you write your question on math site as this seems more of a graph theory problem. –  Robert Koritnik Sep 26 at 11:30
This question appears to be off-topic on this site because it is about mathematics graphs theory. –  Robert Koritnik Sep 26 at 11:32
I've used math to create designs before...I don't see why everyone is voting to close this. Not sure why the downvotes are happening either? It's not a bad quality question, even if the community decides it to be off topic. –  Brendan Sep 26 at 13:33

## migrated from graphicdesign.stackexchange.comSep 26 at 21:42

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