Problem
Research questions and friction points this paper is trying to address.
3-regular graph
Bilu--Linial signing conjecture
eigenvalue
A 3-regular counterexample to the Bilu--Linial signing conjecture
🤖 AI Summary
通过构建一个特定的3正则图并利用四顶点计算和标量递归方法，证明了Bilu-Linial符号猜想对一般正则图不成立。
📝 Abstract
We construct a finite connected simple cubic graph $F$ such that every signing of its edges yields an adjacency matrix with an eigenvalue outside $[-2\sqrt2,2\sqrt2]$. This disproves the Bilu--Linial signing conjecture for general regular graphs. The proof is elementary, using a four-vertex calculation and a scalar recurrence.
Innovation
Methods, ideas, or system contributions that make the work stand out.
cubic graph
eigenvalue
adjacency matrix
signing conjecture
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