The Laplacian matrix is of fundamental importance in the study graphs, networks, random walks on lattices, and arithmetic curves. In certain cases, trace its pseudoinverse appears as only non-trivial term computing some intrinsic graph invariants. Here we a double sum Fn which associated with pseudo inverse for graphs. We investigate asymptotic behavior this n → ∞. Our approach based classical ...

Induction motors (IMs) are commonly used in various industrial applications. To improve energy consumption efficiency, a reliable IM health condition monitoring system is very useful to detect IM fault at its earliest stage to prevent operation degradation, and malfunction of IMs. An intelligent harmonic synthesis technique is proposed in this work to conduct incipient air-gap eccentricity faul...

Let G be a graph with n vertices and m edges. Let λ1, λ2, . . . , λn be the eigenvalues of the adjacency matrix of G, and let μ1, μ2, . . . , μn be the eigenvalues of the Laplacian matrix of G. An earlier much studied quantity E(G) = ∑ni=1 |λi | is the energy of the graph G. We now define and investigate the Laplacian energy as LE(G) = ∑ni=1 |μi − 2m/n|. There is a great deal of analogy between...

In this paper, we investigate how the Laplacian coefficients changed after some graph transformations. So, I express some results about Laplacian coefficients ordering of graphs, focusing our attention to the bicyclic graphs. Finally, as an application of these results, we discuss the ordering of graphs based on their Laplacian like energy.

A light field image generates a set of focusing images at different depth levels. When we reconstruct an allfocused image, we have to identify in-focused regions of the stack images. To address this problem, we propose a method to detect in-focused image regions. We employ sum-modified-laplacian and weight harmonic variance algorithms to solve the problem. The proposed method provides a focus m...