论文标题
标准化的拉普拉斯人获得图形
Normalized Laplacians for Gain Graphs
论文作者
论文摘要
我们提出了标准化的laplacian矩阵$ \ mathcal {l}（φ）$的概念，以详细研究其属性，并在此过程中提供了见解和反描述。我们为$ \ MATHCAL {l}（φ）$的特征值建立界限，并表征平等所保留的图形类。还研究了平衡性，两人的关系及其与$ \ Mathcal {l}（φ）$的频谱的连接之间的关系。此外，我们将特征值交织的边缘版本扩展到增益图。因此，我们确定$ \ Mathcal {l}（φ）$的特征多项式的系数。
We propose the notion of normalized Laplacian matrix $\mathcal{L}(Φ)$ for a gain graphs and study its properties in detail, providing insights and counterexamples along the way. We establish bounds for the eigenvalues of $\mathcal{L}(Φ)$ and characterize the classes of graphs for which equality holds. The relationships between the balancedness, bipartiteness, and their connection to the spectrum of $\mathcal{L}(Φ)$ are also studied. Besides, we extend the edge version of eigenvalue interlacing for the gain graphs. Thereupon, we determine the coefficients for the characteristic polynomial of $\mathcal{L}(Φ)$.
