# A catalog of 4-regular and (2;4)-regular matchstick graphs

## TL;DR

This paper catalogs known examples of 4-regular and (2;4)-regular matchstick graphs, detailing their structures and vertex counts, contributing to the understanding of these specific geometric graph classes.

## Contribution

It provides the first comprehensive collection of known 4-regular and (2;4)-regular matchstick graphs with specified vertex ranges, expanding the catalog of such geometric graphs.

## Key findings

- Known 4-regular matchstick graphs with 63-70 vertices
- Examples of (2;4)-regular matchstick graphs with fewer than 42 vertices
- Detailed enumeration of specific graph configurations

## Abstract

The first part (page 1 - 7) of this article presents the currently known examples of 4-regular matchstick graphs with 63 - 70 vertices. The second part (page 8 - 15) presents the currently known examples of $(2;4)$-regular matchstick graphs with less than 42 vertices which contain only two vertices of degree 2.