Matroids that classify forests

TL;DR

This paper demonstrates that binary matroids derived from adjacency matrices uniquely identify trees and forests up to isomorphism, providing a matroid-theoretic perspective on graph classification.

Contribution

It introduces a novel approach linking binary matroids to the classification of trees and forests, highlighting a new perspective in graph theory.

Findings

Binary matroids from adjacency matrices classify trees and forests uniquely.

Elementary arguments establish the isomorphism classification.

Provides a matroid-theoretic framework for graph identification.

Abstract

Elementary arguments show that a tree or forest is determined (up to isomorphism) by binary matroids defined using the adjacency matrix.