论文标题
从同步图理论中从加权到未加权图
From weighted to unweighted graphs in Synchronizing Graph Theory
论文作者
论文摘要
提出了一种与加权图相关联的未加权图的方法，以便与两个图相关的库拉莫托同质模型的线性稳定平衡重合，即系统的平衡$ \dotθ_i= \ sum_ = \ sum_ $ J $在相应的图中相邻。结果，线性稳定平衡的存在被证明是NP-HARD，这是R. Taylor在2015年的猜想，并且最小程度的新下限是确保发现同步的最低程度。
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.
