[Concept Dependency] Edge Regular Lattice Graph

[Johannes C. Mayer]

This is a Concept Dependency Post. It may not be worth reading on its own, out of context. See the backlinks at the bottom to see which posts use this concept.

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Also known as periodically labeled lattice graphs in graph theory.

Here is a concrete Edge Regular Lattice Graph:

In this graph, the following pattern is repeating locally:

So a Edge Regular Lattice Graph is a Lattice graph $G$, such that in the natural embedding of $G$, each edge label points in the same direction from the perspective of every vertex. Also, the number of edge labels is twice the number of dimensions.

Above we have 4 edge labels in the 2D lattice graph. One for each direction. In a 3D lattice graph, we would have 6 edge labels.

[Emrik]

Oh cool. Another way of embedding higher dimensions in 2D. Edges don’t have to visually line up as long as you label them. And if some dimension (eg ‘z’) is very rarely used, it takes up much less cognitive space compared to if you tried to represent it on equal terms as all other dimensions (eg as in a spatial visualisation). Not sure what I’ll use it for yet tho.