On the smallest parallel quadrangulation with minimum degree 3

TL;DR

This paper investigates the minimal size of a specific type of quadrangulation with minimum degree 3 and parallel edges, narrowing down the possible number of vertices from between 11 and 14 to at least 12.

Contribution

It establishes a new lower bound of 12 vertices for the smallest such quadrangulation, refining previous bounds.

Findings

Order of the smallest quadrangulation is at least 12 vertices.

Narrowed the possible range from 11-14 to 12-14.

Contributes to the classification of minimal quadrangulations with parallel edges.

Abstract

The identity of the smallest quadrangulation with minimum degree 3 also containing parallel edges is unknown. However, it has already been determined that its order (the number of vertices) is between 11 and 14. This paper narrows this domain by showing that the order is at least 12.