论文标题
使用堂兄顶点的几个图形矩阵的宇宙构造
Cospectral constructions for several graph matrices using cousin vertices
论文作者
论文摘要
图形可以根据某些规则与矩阵关联，我们可以找到相对于该矩阵的图的频谱。如果两个图具有相同的频谱，则两个图形是共同的。共光图的构造有助于我们建立有关频谱未保留的结构信息的模式。我们概括了以前为距离拉普拉斯矩阵给出的既定图的构造，以概括为较大的图形家族。此外，我们表明，通过适当的假设，这种广义的结构扩展到邻接矩阵，组合拉普拉斯矩阵，无符号的Laplacian矩阵，归一化的Laplacian矩阵和距离矩阵。
Graphs can be associated with a matrix according to some rule and we can find the spectrum of a graph with respect to that matrix. Two graphs are cospectral if they have the same spectrum. Constructions of cospectral graphs help us establish patterns about structural information not preserved by the spectrum. We generalize a construction for cospectral graphs previously given for the distance Laplacian matrix to a larger family of graphs. In addition, we show that with appropriate assumptions this generalized construction extends to the adjacency matrix, combinatorial Laplacian matrix, signless Laplacian matrix, normalized Laplacian matrix, and distance matrix.
