A four-vertex, quadratic, spanning forest polynomial identity

TL;DR

This paper extends the classical Dodgson identity to a quadratic identity involving spanning forest polynomials with four marked vertices, broadening the understanding of polynomial identities in graph theory.

Contribution

It introduces a new quadratic identity for spanning forest polynomials with four marked vertices, generalizing the classical Dodgson identity.

Findings

Proves a new quadratic identity for four marked vertices

Generalizes the classical Dodgson identity

Enhances understanding of spanning forest polynomial relations

Abstract

The classical Dodgson identity can be interpreted as a quadratic identity of spanning forest polynomials, where the spanning forests used in each polynomial are defined by how three marked vertices are divided among the component trees. We prove an analogous result with four marked vertices.