On the normalized Laplacian energy and general Randić index R-1 of graphs
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This paper considers the energy of a simple graph with respect to its normalized Laplacian eigenvalues, which is called the L-energy, and provides upper and lower bounds for L- energy based on its general Randic index R-1(G).About:
This article is published in Linear Algebra and its Applications.The article was published on 2010-07-15 and is currently open access. It has received 122 citations till now. The article focuses on the topics: Resistance distance & Laplacian matrix.read more
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Assortativity in Complex Networks
TL;DR: The concept of assortativity is surveyed, starting from its original definition by Newman in 2002, and a new scope of research is provided to incorporate directed graphs and weighted links.
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On Randić energy
TL;DR: In this paper, the Randic matrix R = ( r i j ) of a graph G whose vertex v i has degree d i is defined by R i j = 1 / d i d j if the vertices v i and v j are adjacent and r i J = 0 otherwise.
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Beyond the Zagreb indices
TL;DR: The two Zagreb indices M1 and M2 are vertex-degree-based graph invariants that have been introduced in the 1970s and extensively studied ever since and in the last few years, a var...
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On the spectrum of the normalized Laplacian of iterated triangulations of graphs
TL;DR: The spectra of the normalized Laplacian of iterated triangulations of a generic simple connected graph are determined and closed-forms for their multiplicative degree-Kirchhoff index, Kemeny's constant and number of spanning trees are found.
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Book
Table of Integrals, Series, and Products
TL;DR: Combinations involving trigonometric and hyperbolic functions and power 5 Indefinite Integrals of Special Functions 6 Definite Integral Integral Functions 7.Associated Legendre Functions 8 Special Functions 9 Hypergeometric Functions 10 Vector Field Theory 11 Algebraic Inequalities 12 Integral Inequality 13 Matrices and related results 14 Determinants 15 Norms 16 Ordinary differential equations 17 Fourier, Laplace, and Mellin Transforms 18 The z-transform
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Matrix Analysis
Roger A. Horn,Charles R. Johnson +1 more
TL;DR: In this article, the authors present results of both classic and recent matrix analyses using canonical forms as a unifying theme, and demonstrate their importance in a variety of applications, such as linear algebra and matrix theory.
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Spectral Graph Theory
TL;DR: Eigenvalues and the Laplacian of a graph Isoperimetric problems Diameters and eigenvalues Paths, flows, and routing Eigen values and quasi-randomness
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