论文标题
连接图的距离Seidel矩阵
Distance Seidel matrix of a connected graph
论文作者
论文摘要
对于连接的图形$ g $，我们介绍了与其距离相关的新图矩阵的概念和seidel矩阵，称为距离seidel矩阵$ \ mathcal {d}^s（g）$。假设$ \ Mathcal {d}^s（g）$ be $ \ partial_ {1}^{s}（g）\ geq \ cdots \ geq \ geq \ geq \ geq \ geq \ geq \ geq \ geq \ geq \ partial_ {n}^{s}（s}（g）（g）。我们用$ \ partial_ {1}^{s}（g）= 3来表征所有连接的图形。$另外，我们确定了距离Seidel Spectral Radius和距离Seidel Energy的不同边界。由于边缘删除，我们研究了完整两分图的距离Seidel能量变化。此外，我们获得了不同图形操作的距离Seidel光谱，例如联接，笛卡尔产品，词典摄影产品以及一单图形和延伸的双层盖图。我们为距离Seidel Cosectral和距离Seidel积分图的各种家族作为应用。
For a connected graph $G$, we present the concept of a new graph matrix related to its distance and Seidel matrix, called distance Seidel matrix $\mathcal{D}^S(G)$. Suppose that the eigenvalues of $\mathcal{D}^S(G)$ be $\partial_{1}^{S}(G) \geq \cdots \geq \partial_{n}^{S}(G).$ In this article, we establish a relationship between distance Seidel eigenvalues of a graph with its distance and adjacency eigenvalues. We characterize all the connected graphs with $\partial_{1}^{S}(G)= 3.$ Also, we determine different bounds for the distance Seidel spectral radius and distance Seidel energy. We study the distance Seidel energy change of the complete bipartite graph due to the deletion of an edge. Moreover, we obtain the distance Seidel spectra of different graph operations such as join, cartesian product, lexicographic product, and unary operations like the double graph and extended double cover graph. We give various families of distance Seidel cospectral and distance Seidel integral graphs as an application.
