# Site-specific Gordian distances of spatial graphs

## TL;DR

This paper introduces and analyzes the concept of site-specific Gordian distances in spatial graphs, determining these distances in specific cases and applying the results to links and the puzzle ring problem.

## Contribution

It defines the site-specific Gordian distance, computes it for certain spatial embeddings, and applies covering space theory to solve related problems in knot theory.

## Key findings

- Determined site-specific Gordian distances for Milnor links and trivial links.
- Applied covering space theory to compute these distances.
- Connected the concept to the puzzle ring problem.

## Abstract

A site-specific Gordian distance between two spatial embeddings of an abstract graph is the minimal number of crossing changes from one to another where each crossing change is performed between two previously specified abstract edges of the graph. It is infinite in some cases. We determine the site-specific Gordian distance between two spatial embeddings of an abstract graph in certain cases. It has an application to puzzle ring problem. The site-specific Gordian distances between Milnor links and trivial links are determined. We use covering space theory for the proofs.