For any simple connected undirected graph, it is well known that the Kirchhoff and multiplicative degree-Kirchhoff indices can be computed using the Laplacian matrix. We show that the same is true for the additive degree-Kirchhoff index and give a compact Matlab program that computes all three Kirchhoffian indices with the Laplacian matrix as the only input.

In this paper an estimator for speech enhancement based on Laplacian Mixture Model has been proposed. The proposed method, estimates the complex DFT coefficients of clean speech from noisy speech using the MMSE  estimator, when the clean speech DFT coefficients are supposed mixture of Laplacians and the DFT coefficients of  noise are assumed zero-mean Gaussian distribution. Furthermore, the MMS...

Let $S(G)$ be the Seidel matrix of a graph $G$ of order $n$ and let $D_S(G)=diag(n-1-2d_1, n-1-2d_2,ldots, n-1-2d_n)$ be the diagonal matrix with $d_i$ denoting the degree of a vertex $v_i$ in $G$. The Seidel Laplacian matrix of $G$ is defined as $SL(G)=D_S(G)-S(G)$ and the Seidel signless Laplacian matrix as $SL^+(G)=D_S(G)+S(G)$. The Seidel signless Laplacian energy $E_{SL^+...

A new existence result is obtained for nonautonomous second order Hamiltonian systems with (q, p)-Laplacian by using the minimax methods.

The standard notion of the Laplacian of a graph is generalized to the setting of a graph with the extra structure of a “transmission” system. A transmission system is a mathematical representation of a means of transmitting (multi-parameter) data along directed edges from vertex to vertex. The associated transmission graph Laplacian is shown to have many of the former properties of the classica...

This paper presents a general methodology to calculate the resiliency of complex engineered systems based on complex network theory. Graph spectral theory has been used simultaneously with complex network theory for years. Resiliency is a key driver in how systems are developed to operate in an expected operating environment, and how systems change and respond to the environments in which they ...

a spanning tree of graph g is a spanning subgraph of g that is a tree. in this paper, we focusour attention on (n,m) graphs, where m = n, n + 1, n + 2 and n + 3. we also determine somecoefficients of the laplacian characteristic polynomial of fullerene graphs.

in this paper, we establish some results on the existence of at least three weak solutions for adirichlet problem involving p-laplacian using a variational approach.

In network science, the interplay between dynamical processes and the underlying topologies of complex systems has led to a diverse family of models with different interpretations. In graph signal processing, this is manifested in the form of different graph shifts and their induced algebraic systems. In this paper, we propose the unifying Z-Laplacian framework, whose instances can act as graph...

this work concerns the study of existence and uniqueness to heat equation with fractional laplacian dierentiation in extended colombeau algebra.