Suppose μ1, μ2, ... , μn are Laplacian eigenvalues of a graph G. The Laplacian energy of G is defined as LE(G) = ∑n i=1 |μi − 2m/n|. In this paper, some new bounds for the Laplacian eigenvalues and Laplacian energy of some special types of the subgraphs of Kn are presented. AMS subject classifications: 05C50

Cerebral language lateralization can be assessed in several ways. In healthy subjects, functional MRI (fMRI) during performance of a language task has evolved to be the most frequently applied method. Functional transcranial Doppler (fTCD) may provide a valid alternative, but has been used rarely. Both techniques have their own strengths and weaknesses and as a result may be applied in differen...

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.

RNA stem-loop structures play an important role in almost every step of the viral replication cycle. In this contribution, a mathematical analysis is performed on large dataset secondary structure elements coding regions viruses by using topological indices that capture Laplacian eigenvalues associated graph representations and thereby enable structural classification, supplemented folding ener...

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 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...

In this paper, we investigate the Laplacian, i.e., the normalized Laplacian tensor of a k-uniform hypergraph. We show that the real parts of all the eigenvalues of the Laplacian are in the interval [0, 2], and the real part is zero (respectively two) if and only if the eigenvalue is zero (respectively two). All the H+-eigenvalues of the Laplacian and all the smallest H+-eigenvalues of its sub-t...

In this paper, we introduce a new class of nonlocal p-Laplacian operators that interpolate between non-local Laplacian and infinity Laplacian. These operators are discrete analogous of the game p-laplacian operators on Euclidean spaces, and involve discrete morphological gradient on graphs. We study the Dirichlet problem associated with the new p-Laplacian equation and prove existence and uniqu...