Web12 de jul. de 2013 · 1 Answer. For a start, there's the complements of the paths. (If the Laplacian eigenvalues of a graph are all simple, then so are the eigenvalues of its complement.) Most regular graphs have only simple eigenvalues; in particular if my sage computations can be trusted then 6 of 21 cubic graphs on 10 vertices have only simple … WebThe problem (2) is to choose edge weights on a graph, subject to some constraints, in order to minimize a convex function of the positive eigenvalues of the associated Laplacian matrix. We can also handle the case of maximizing a concave function φof the positive Laplacian eigenvalues, by minimizing −ψover w∈ W.

On the Approximation of Laplacian Eigenvalues in Graph …

Web20 de mar. de 2024 · We obtain a relationship between the Laplacian energy and the distance Laplacian energy for graphs with diameter 2. We obtain lower bounds for the … Webgraph theory terminology in Section 2, an intuitive understanding of the Laplacian of a graph in Section 3, an analysis of the range of eigenvalues of the Laplacian in Section … cwnd msdn

Mathematics Free Full-Text On the Generalized Distance Energy …

WebThe complex case is considered to allow unconstrained phase randomization in the transformed domain, hence we define a Hermitian Laplacian matrix that models the … WebLaplacian integral graphs is Laplacian integral. These are done in Section 4. The Laplacian eigenvalues and eigenvectors of the lexicographic product of graphs have been described in general, though not explicitly. In [24], Neumann and Pati have characterized the Laplacian spectra of graphs G[T, Gi, . . . , Gn], where T is a tree of order n and ... WebIn this paper we consider the energy of a simple graph with respect to its Laplacian eigenvalues, and prove some basic properties of this energy. In particular, we find the minimal value of this energy in the class of all connected graphs on n vertices ( n = 1, 2, ...). cwn dividend 2022