2-控制数与上中位度：Graffiti.pc 猜想387的证明
The 2-Domination Number and the Upper Median Degree: A Proof of Graffiti.pc Conjecture 387
AI总结：
本文证明非空有限简单图的2-控制数上界为n - m(G) + 1，解决了Graffiti.pc猜想387，且无需原猜想的连通性假设，证明依赖补图与多项式族工具。
AI中文摘要：
设G为阶数n的非空有限简单图，m(G)为其度序列的上中位。本文证明2-控制数满足γ₂(G) ≤ n - m(G) + 1，从而证明了Graffiti.pc猜想387。实际上该论证对所有非空有限简单图均成立，原表述中的连通性假设不必要。证明使用补图及编码选定非邻域的最小线性相关多项式族。
英文摘要：
Let G be a nonempty finite simple graph of order n, and let m(G) be the upper median of its degree sequence. We prove that the 2-domination number satisfies gamma_2(G) <= n - m(G) + 1. This proves Graffiti.pc Conjecture 387. In fact, the argument establishes the inequality for every nonempty finite simple graph, so the connectedness hypothesis in the original formulation is unnecessary. The proof uses the complement graph and a minimally linearly dependent family of polynomials encoding selected nonneighborhoods.
