同步图论中从赋权图到赋权图
From weighted to unweighted graphs in Synchronizing Graph Theory
摘要：
提出了一种将未赋权图与赋权图相关联的方法，使得关联到这两个图的Kuramoto齐次模型的线性稳定平衡点重合，即，系统$\dotθ_i = \sum_{j \sim i} \sin(θ_{j}-θ_j)$的平衡，其中$i\sim j$表示顶点$i$和$j$在相应的图中相邻。由此证明了线性稳定平衡点的存在性是NP-Hard的。Taylor在2015年提出了一个新的最小度的下界，并给出了保证同步的最小度的下界.
英文摘要：
A way to associate unweighted graphs from weighted ones is presented, such that linear stable equilibria of the Kuramoto homogeneous model associated to both graphs coincide, i.e., equilibria of the system $\dotθ_i = \sum_{j \sim i} \sin(θ_{j}-θ_j)$, where $i\sim j$ means vertices $i$ and $j$ are adjacent in the corresponding graph. As a consequence, the existence of linearly stable equilibrium is proved to be NP-Hard as conjectured by R. Taylor in 2015 and a new lower bound for the minimum degree that ensures synchronization is found.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
