The dynamic analysis of structures using the nite element method leads to very large eigenvalue problems. Condensation is often required to reduce the number of degrees of freedom of these problems to manageable size. The (statically or dynamically) condensed problem can be considered as linearization of a matrix eigenvalue problem which is nonlinear with respect to the eigenparameter. As a con...

In this paper, we show the evaluation of the spectral radius for node degree as the basis to analyze the variation in the node degrees during the evolution of scale-free networks and small-world networks. Spectral radius is the principal eigenvalue of the adjacency matrix of a network graph and spectral radius ratio for node degree is the ratio of the spectral radius and the average node degree...

The reconfiguration graph R k ( G ) for the -colorings of a has as vertex set all possible and two colorings are adjacent if they differ in color exactly one . Let d , ? 1 be integers such that + We prove every ? > 0 with n vertices maximum average degree ? diameter O log ? This significantly strengthens several existing results.

All dynamical systems of biological interest—be they food webs, regulation of genes, or contacts between healthy and infectious individuals—have complex network structure. Wigner’s semicircular law and Girko’s circular law describe the eigenvalues of systems whose structure is a fully connected network. However, these laws fail for systems with complex network structure. Here we show that in th...

In this paper, we study synchronization of complex random networks of nonlinear oscillators, with specifiable expected degree distribution. We review a sufficient condition for synchronization and a sufficient condition for desynchronization, expressed in terms of the eigenvalue distribution of the Laplacian of the graph and the coupling strength. We then provide a general way to approximate th...

in this paper, we present some inequalities for the co-pi index involving the some topological indices, the number of vertices and edges, and the maximum degree. after that, we give a result for trees. in addition, we give some inequalities for the largest eigenvalue of the co-pi matrix of g.

This paper presents a combined adaptive finite element method with an iterative algebraic eigenvalue solver for a symmetric eigenvalue problem of asymptotic quasi-optimal computational complexity. The analysis is based on a direct approach for eigenvalue problems and allows the use of higher-order conforming finite element spaces with fixed polynomial degree. The asymptotic quasi-optimal adapti...