New examples of Brunnian theta graphs
Byoungwook Jang, Anna Kronaeur, Pratap Luitel, Daniel Medici, Scott A., Taylor, Alexander Zupan

TL;DR
This paper introduces a new family of Brunnian theta graphs, expanding the known examples by linking them to a subgroup of the pure braid group, and proves their non-isotopy.
Contribution
It presents a novel family of Brunnian theta graphs parameterized by a subgroup of the pure braid group, demonstrating their infinite non-isotopic instances.
Findings
New family of Brunnian theta graphs constructed
Infinitely many non-isotopic examples proven
Connection established with pure braid group subgroup
Abstract
The Kinoshita graph is the most famous example of a Brunnian theta graph, a nontrivial spatial theta graph with the property that removing any edge yields an unknot. We produce a new family of diagrams of spatial theta graphs with the property that removing any edge results in the unknot. The family is parameterized by a certain subgroup of the pure braid group on four strands. We prove that infinitely many of these diagrams give rise to non-isotopic Brunnian theta graphs.
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