New minimal (4; n)-regular matchstick graphs

TL;DR

This paper presents the smallest known (4;n)-regular matchstick graphs for 4 ≤ n ≤ 11, expanding the understanding of such geometric graph configurations.

Contribution

It introduces the latest minimal (4;n)-regular matchstick graphs for 4 ≤ n ≤ 11, with the fewest vertices known to date.

Findings

New minimal (4;n)-regular matchstick graphs for 4 ≤ n ≤ 11

Reduced the number of vertices needed for these graphs

Enhanced understanding of geometric graph configurations

Abstract

A matchstick graph is a graph drawn with straight edges in the plane such that the edges have unit length, and non-adjacent edges do not intersect. We call a matchstick graph ($m;n)$-regular if every vertex has only degree $m$ or $n$. In this article the authors present the latest known $(4;n)$-regular matchstick graphs for $4\leq n\leq11$ with a minimum number of vertices.