5
votes
0answers
77 views

Tilings of the Hyperbolic plane

Given a tiling of the hyperbolic plane projected onto a unit disc such as this which can be considered as a graph. I then define some functions: $f(r) =$ number of graph nodes contained within the a ...
2
votes
1answer
44 views

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 ...
0
votes
1answer
119 views

“Simmetric” connected k-regular bipartite graph

Let $G$ be a k-regular bipartite graph with $k > 0$. Then it is known that the two sets which partition the vertex set of $G$ have the same cardinality. However I am interested in connected ...
6
votes
2answers
416 views

Checkerboard-Coloring $\mathbb{Z}^2$

If every square of the unit square lattice in the plane is colored black or white according to a set of rules, is there a way to find the maximum asymptotic ratio $r_n$ of the number of black squares ...