For a graph, the least signless Laplacian eigenvalue is the least eigenvalue of its signless Laplacian matrix. This paper investigates how the least signless Laplacian eigenvalue of a graph changes under some perturbations, and minimizes the least signless Laplacian eigenvalue among all the nonbipartite graphs with given matching number and edge cover number, respectively.

For a graph, the least signless Laplacian eigenvalue is the least eigenvalue of its signless Laplacian matrix. This paper investigates how the least signless Laplacian eigenvalue of a graph changes under some perturbations, and minimizes the least signless Laplacian eigenvalue among all the nonbipartite graphs with given matching number and edge cover number, respectively.

The Laplacian spread of a graph is defined to be the difference between the largest eigenvalue and the second smallest eigenvalue of the Laplacian matrix of the graph. In this paper, we investigate Laplacian spread of graphs, and prove that there exist exactly five types of tricyclic graphs with maximum Laplacian spread among all tricyclic graphs of fixed order.

recently, we have used the symmetric bracket of vector fields, and developed the notion of the symmetric derivation. using this machinery, we have defined the concept of symmetric curvature. this concept is natural and is related to the notions divergence and laplacian of vector fields. this concept is also related to the derivations on the algebra of symmetric forms which has been discus...

The variation of the instantaneous power versus distance for a narrowband channel is an important parameter in modern digital systems, relevant for variations during a burst and for power control algorithms. This paper gives the statistical distribution for the power gradient, both in decibels and in natural units for a Rayleigh fading channel. The former has been known for some time to be Stud...

The graph Laplacian plays key roles in information processing of relational data, and has analogies with the Laplacian in differential geometry. In this paper, we generalize the analogy between graph Laplacian and differential geometry to the hypergraph setting, and propose a novel hypergraph pLaplacian. Unlike the existing two-node graph Laplacians, this generalization makes it possible to ana...

We present an adaptive fast multipole method for inverting the square root of the Laplacian in two dimensions. Solving this problem is the dominant computational cost in many applications arising in electrical engineering, geophysical fluid dynamics, and the study of thin films. It corresponds to the evaluation of the field induced by a planar distribution of charge or vorticity. Our algorithm ...

We analyze the spectral distribution of the adjacency matrix and the graph Laplacian for a wide variety of random trees. Using soft arguments which seem to be applicable in a wide variety of settings, we show that the empirical spectral distribution for a number of random tree models, converges to a constant (model dependent) distribution. We also analyze the kernel of the spectrum and prove as...

where (b) holds by applying chain rule successively, and (c) holds because conditioning reduces entropy. Note that, for a known exponential family distribution, H(Xr | Br(X)) is constant. For examples in a Gaussian, Dirichlet, Gamma, Wishart, Xr is also a function of Br(Xr), meaning H(Xr | Br(X)) = 0. For a Laplacian distribution, H(Xr | Br(X)) = H(Sign(Xr)) = 1. Therefore, we can conclude that...

The threshold model can be used to generate random networks of arbitrary size with given local properties such as the degree distribution, clustering, and degree correlation. We summarize the properties of networks created using the threshold model and present an alternative deterministic construction. These networks are threshold graphs and therefore contain a highly compressible layered struc...