Department of Mathematical Sciences
Discrete Seminar
Thursday, February 12th, 2026
12:00PM-12:50PM
Olin Hall 218
Speaker: Joseph Fehribach, WPI
Title: An Update on Kirchhoff Graphs
Abstract: Given a set of n vectors in any vector space over the rationals, suppose that k < n are linearly independent. Kirchhoff graphs are vector graphs (graphs whose edges are these vectors), whose cycles represent the dependencies of these vectors and whose vertex cuts are orthogonal to these cycles. This presentation introduces these graphs and discusses how graph tiling can generate families of Kirchhoff graphs. These families are composed of prime graphs (those having no Kirchhoff subgraphs), and composite graphs (not prime), all generated by a set of fundamental Kirchhoff graphs with multiplicity m* . Finally, this talk discusses a conjecture for computing the value of m* without actually constructing these fundamental Kirchhoff graphs. This work depends on the numerical construction of Kirchhoff graphs.