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).

Curvy or Curly keyboard layouts

My journey into the world of DIY Ergonomic Mechanical Keyboards began when my Microsoft Natural Ergonomic Keyboard 4000 started to fail. That has a very slight curve to the alphabet block's rows, which became more pronounced in later designs like the Microsoft Sculpt Ergonomic Keyboard (see Wikipedia). However, these all have the traditional row stagger which gives the right hand comfortable (diagonal) columns of keys per finger, but not the left.

In the DIY mechanical keyboard world column based layouts and orthonormal are popular (keys in a grid), but there is another solution which at first glance preserves the traditional row stagger: The symmetric katana stagger, originally popularised by Baris Tosun aka RominRonin's Kanata keyboards as early as 2015. Well, what if you combined that with a curve to each row?

This looks like a row stagger, but there are well defined columns for each finger!