The sl(2)-weight system at c = 3/8 for graphs

TL;DR

This paper introduces a new 4-invariant extending a specialized $ ext{sl}(2)$-weight system at $c=3/8$, which satisfies a deletion-contraction relation, advancing graph invariants in knot theory.

Contribution

It constructs a novel 4-invariant that generalizes a specific $ ext{sl}(2)$-weight system at $c=3/8$ with a simple recursive relation.

Findings

Defines a new 4-invariant for graphs.

Extends a specialization of the $ ext{sl}(2)$-weight system.

Satisfies a deletion-contraction relation.

Abstract

We construct a 4-invariant that extends a specialization of the $\mathfrak{sl}(2)$-weight system at $c = \frac 38$, and satisfies a simple deletion-contraction relation.