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pro vyhledávání: '"McInnis, Ian Malcolm Johnson"'
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 unicyclic graphs whose cycle is a triangle. Partial results are given on th
Externí odkaz:
http://arxiv.org/abs/2304.13020
A weighted graph $\phi G$ encodes a finite metric space $D_{\phi G}$. When is $D$ totally decomposable? When does it embed in $\ell_1$ space? When does its representing matrix have $\leq 1$ positive eigenvalue? We give useful lemmata and prove that t
Externí odkaz:
http://arxiv.org/abs/2304.13018
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 through a motivating matrix completion problem. We give a concise proof,
Externí odkaz:
http://arxiv.org/abs/2304.09335