Binary matroids and local complementation

TL;DR

This paper introduces a binary matroid linked to a looped simple graph that classifies the graph's local equivalence, relates to delta-matroids and isotropic systems, and connects to interlace polynomials via a parametrized Tutte polynomial.

Contribution

It presents a new binary matroid construction that captures graph equivalence classes and relates to various graph invariants and polynomials.

Findings

Classifies graphs up to local equivalence

Determines associated delta-matroids and isotropic systems

Links Tutte polynomial to interlace polynomials

Abstract

We introduce a binary matroid M(IAS(G)) associated with a looped simple graph G. M(IAS(G)) classifies G up to local equivalence, and determines the delta-matroid and isotropic system associated with G. Moreover, a parametrized form of its Tutte polynomial yields the interlace polynomials of G.