3 papers
math.CO2023
Graphical distances & inertia
Jeffrey Cheng, Ian Malcolm Johnson McInnis, Matthew Yee
We study the inertia of distance matrices of weighted graphs. Our novel congruence-based proof of the inertia of weighted trees extends to a proof for the inertia of weighted unicy…
math.CO2023
Isometric embedding and spectral constraints for weighted graph metrics
Jeffrey Cheng, Ian Malcolm Johnson McInnis, Matthew Yee
A weighted graph encodes a finite metric space . When is totally decomposable? When does it embed in space? When does its representing matrix have $\leq 1…
math.CO2023
Characterizing and generalizing cycle completable graphs
Maria Chudnovsky, Ian Malcolm Johnson McInnis
The family of cycle completable graphs has several cryptomorphic descriptions, the equivalence of which has heretofore been proven by a laborious implication-cycle that detours thr…