Enumeration and Generation of Simple Unlabelled Graphs

Title

Enumeration and Generation of Simple Unlabelled Graphs

Subject

Mathematics

Description

Tropicalisation of Conics Poster

Creator

Xavier Gasper, Ibrahim Adnan Khan

Abstract

We investigated the matroid of the degree-d Macaulay matrix of a conic polynomial, a problem with applications in tropical geometry. Employing graph-theoretic methods and Macaulay2 programs, we analysed the 0-determinant submatrices of the Macaulay matrix satisfying the Fink-Giansiracusa condition. We uncovered a novel method for generating singular submatrices satisfying this condition, in arbitrary degree, through the embedding of singular minors from lower degrees.

Meta Tags

Tropical Geometry, Combinatorics, Linear Algebra

Files

Collection

Mathematics

Citation

Xavier Gasper, “Enumeration and Generation of Simple Unlabelled Graphs,” URSS SHOWCASE, accessed November 2, 2025, https://urss.warwick.ac.uk/items/show/910.