Small girth 8 graphs for keyboard wiring

This post is a less interesting follow up to my recent catalogue of girth 6 graphs for keyboard wiring, which give 4-key roll over (4KRO). As explained in my first keyboard and Graph Theory blog post, the idea here is applying these graphs to the design of diode-free computer keyboards where the bipartite matrix becomes a sparse scanning matrix. Using a graph with girth 8 gives 6-key rollover (6KRO), high enough not to be a practical limitation, unless perhaps for stenography? Sadly from a mathematical point of view these are mostly subgraphs of the Tutte Coxetter Graph (aka the Tutte 8 Cage), the unique smallest trivalent graph of girth 8.

5-way switch in a diode-free Graph Theory keyboard

My first post about keyboards introduced the idea of Graph Theory applied to keyboard wiring. I have since used the girth 8 Tutte-Coxeter Graph to build a 6KRO keyboard (the Gamma Omega TC36K), and several girth 6 graphs to build 4KRO keyboards (see table of girth 6 graphs for keyboards in this recent post). But what about other kinds of switches like 3-way jog dials (up/down/push) or 5-way directional buttons (up/down/left/right/push)?

Almost a year of DIY Mechanical Keyboards

I did a retrospective in August of how looking for a replacement keyboard led up to building a Ergonomic Mechanical Keyboard with a self-designed PCB roughly six month later (the diode-free Graph Theory based Gamma Omega TC36K). That design is beginner friendly, and went smoothly. In October someone else made a pair of them - nice!

A pair of Gamma Omega TC36K keyboards

So what have I done with keyboards since? Just designed and built three more...

Slump52 - an ErgoMech keyboard with number pad

Up until now, I have had three different keyboard PCBs fabricated to my own design - all diode-free using Graph Theory. The Gamma Omega TC36K, the Gamma Omega Hesse, and the Forager Acid, with 36, 36 and 34 keys respectively. They've been getting smaller. Well now for something bigger, requested by our nine year old: They want a keyboard with more keys, and deserve smaller keys. Here is the Slump52!

Slump52 keyboard PCB design in KiCad

Small girth 6 graphs for keyboard wiring

This post is an expanded and reworked version of the table in my first keyboards and Graph Theory blog post, listing the best (in terms of maximal number of edges) girth 6 bipartite small graph(s). I added many of these to the House of Graphs database, and then in October the mathematician Steven Van Overberghe added a few more. My interest here is applying the graphs to the design of diode-free computer keyboards where the bipartite matrix becomes a sparse scanning matrix, and girth 6 becomes 4-key rollover (4KRO).