signless Laplacian
时间: 2023-10-18 09:05:21 浏览: 70
On distance signless Laplacian spectral radius of graphs
The signless Laplacian of a graph is a matrix that is derived from the Laplacian matrix of the graph. It is defined as the matrix Q = D + A, where D is the diagonal matrix of the degrees of the vertices, and A is the adjacency matrix of the graph.
The signless Laplacian has several interesting properties and applications in graph theory and related fields. For example, it can be used to study the stability and robustness of networks, as well as to derive upper bounds on the chromatic number of a graph.
Furthermore, the eigenvalues of the signless Laplacian are closely related to the degree sequence and the connectivity properties of the graph. In particular, the smallest eigenvalue of Q is always non-negative, and it is zero if and only if the graph is disconnected.
Overall, the signless Laplacian provides a powerful tool for analyzing the structure and properties of graphs, and it has numerous applications in various areas of mathematics, computer science, and engineering.
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