Here we investigate how the spectrum of the normalized graph Laplacian gets affected by certain graph operations like motif duplication and graph (or motif) joining.

In this paper we introduce the k’th isoperimetric constant of a directed graph as the minimum of the mean outgoing normalized flows from a given set of k disjoint subsets of the vertex set of the graph. In this direction we show that the second isoperimetric constant in the general setting coincides with (the mean version of) the classical Cheeger constant of the graph, while for the rest of th...

We present a critical review and analysis of different categories of routing protocols for cognitive radio networks. We first classify the available solutions to two broad categories: those based on full spectrum knowledge (typically used to establish performance benchmarks) and those based on local spectrum knowledge (used for real-time implementation). The full spectrum knowledge based routin...

A graph G is said to be determined by its Q-spectrum if with respect to the signless Laplacian matrix Q , any graph having the same spectrum as G is isomorphic to G. The lollipop graph, denoted by Hn,p, is obtained by appending a cycle Cp to a pendant vertex of a path Pn−p. In this paper, it is proved that all lollipop graphs are determined by their Q -spectra. © 2008 Elsevier B.V. All rights r...

We present a framework based on spectral graph theory that captures the interplay among network topology, system inertia, and generator and load damping in determining overall power grid behavior and performance. Specifically, we show that the impact of network topology on a power system can be quantified through the network Laplacian eigenvalues, and such eigenvalues determine the grid robustn...

We present the spectrum of the (normalized) graph Laplacian as a systematic tool for the investigation of networks, and we describe basic properties of eigenvalues and eigenfunctions. Processes of graph formation like motif joining or duplication leave characteristic traces in the spectrum. This can suggest hypotheses about the evolution of a graph representing biological data. To this data, we...

Complex networks are becoming indispensable parts of our lives. The Internet, wireless (cellular) networks, online social networks, and transportation networks are examples of some well-known complex networks around us. These networks generate an immense range of big data: weblogs, social media, the Internet traffic, which have increasingly drawn attentions from the computer science research co...

FOX-7 (1,1-diamino-2,2-dinitroethylene) recently is expected as a relatively new energetic material with high-performance and low sensitivity. The RHF and MP2 levels and DFT method with B3LYP functional with aug-cc-pVDZ basis set have been used for obtaining equilibrium geometry and Rho function (electron density distribution). By the aid of fundamental physical theorems implemented in the ...