As an application, we obtain some estimates of the eigenvalues of the normalized graph Laplacian by the Ricci curvature of the (k,m)-gluing graph.Shuqin Zhanggrid.67293.39School of MathematicsHunan University 410082 Changsha ChinaYingqing Xiao...
Liu. Noncompact complete riemannian manifolds with dense eigenvalues embedded in the essential spectrum of the Laplacian. Preprint.S. Jitomirskaya and W. Liu. Noncompact Riemannian manifolds with dense eigenvalues embedded in the essential spectrum of the Laplacian. arXiv preprint arXiv:1805.01072, ...
In spectral graph theory, the (adjacency) spectrum of a graph, which is the spectrum of its adjacency matrix, is one of its topologi- cal invariants16. Thus, the spectrum of Af(e) can be used to describe the grain topology. The Laplacian matrix of a graph is defined as the degree ...
Towards the complete structural characterization of a protein folding pathway: the structures of the denatured, transition and native states for the association/folding of two complementary fragments of cleaved chymotrypsin inhibitor 2. Direct evidence for a nucleation-condensation mechanism...
Graph LaplacianSpectral graph theoryProtein modelWe characterize the spectrum of the Laplacian of graphs composed of one or two finite or infinite chains connected to a complete graph. We show the existence of localized eigenvectors of two types, eigenvectors that vanish exactly outside the complete ...
Cheng X., Zho D.: Eigenvalues of the drifted Laplacian on complete metric measure spaces. Commun. Contemp. Math. http://dx.doi.org/10.1142/S0219199716500012.X. Cheng and D. Zhou, Eigenvalues of the drifted Laplacian on complete metric measure spaces, Commun. Contemp. Math. 19 (2017), no...
A graph G is called Q-integral if all the eigenvalues of its signless Laplacian characteristic polynomial QG(x) are integers. In this paper, we give a sufficient and necessary condition for complete r-partite graphs to be Q-integral, from which we construct infinitely many new classes of Q...
Cardone. Complete asymptotic expansions for the eigenvalues of the Dirichlet Laplacian in thin three-dimensional rods. ESAIM. Contr. Op. Ca. Va. 17:3, 887-908 (2011).D. Borisov, G. Cardone. Complete asymptotic expansions for the eigenvalues of the Dirichlet Laplacian in thin three-dimensional...
We introduce the notion of ( k , m )-gluing graph of two complete graphs G n , G n ′ G_n, G_n' and get an accurate value of the Ricci curvature of each edge on the gluing graph. As an application, we obtain some estimates of the eigenvalues of the normalized graph Laplacian ...
Such drawings are related with Laplacian eigenvalues of graphs. This motivates us to study which properties of the algebraic connectivity of graphs carry over to the restricted setting of drawings of graphs with integer coordinates.doi:10.1007/978-3-030-04414-5_42Fabila-Monroy, Ruy...