Zijian Zeng

The Complete Two‑Weight \(\mathbb{Z}/5\mathbb{Z}\) Goemans–Linial Cone

For the weighted Cayley graph on \(\mathbb{Z}/5\mathbb{Z}\) whose difference‑\(\pm1\) edges have weight a and difference‑\(\pm2\) edges have weight b, we determine the uniform‑demand sparsest cut and the Goemans–Linial relaxation for every \(b\ge 0\) with \(a+b>0\). Both values a...

The Complete Two‑Weight \(\mathbb{Z}/5\mathbb{Z}\) Goemans–Linial Cone

For the weighted Cayley graph on \(\mathbb{Z}/5\mathbb{Z}\) whose difference‑\(\pm1\) edges have weight a and difference‑\(\pm2\) edges have weight b, we determine the uniform‑demand sparsest cut and the Goemans–Linial relaxation for every \(b\ge 0\) with \(a+b>0\). Both values a...

Exact Homological Invariants for Closed‑Neighborhood Ideals of Cubes of Broom Graphs

Let \(B(n, m)\) be the broom graph formed from a path \(y_{1},\dots, y_{m}\) by attaching n leaves to \(y_{1}\), and let \(I_{n,m}\) be the closed‑neighborhood ideal of its third graph power. Over an arbitrary field, we determine the projective dimension, Castelnuovo–Mumford regu...