Reduced Wu and Generalized Simon Invariants for Spatial Graphs

TL;DR

This paper introduces new invariants for spatial graphs based on Wu and Simon invariants, which help determine graph chirality and establish lower bounds for crossing numbers in embeddings.

Contribution

It presents novel invariants for spatial graphs that extend Wu and Simon invariants, providing tools to analyze graph chirality and crossing number bounds.

Findings

Certain graphs are proven to be intrinsically chiral using these invariants.

The invariants establish lower bounds for the minimal crossing number of embedded graphs.

Abstract

We introduce invariants of spatial graphs related to the Wu invariant and the Simon invariant, and apply them to prove that certain graphs are intrinsically chiral, and to obtain lower bounds for the minimal crossing number of embedded graphs.