New minimal (4; n)-regular matchstick graphs

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.