Topic
Spectral graph theory
About: Spectral graph theory is a research topic. Over the lifetime, 1334 publications have been published within this topic receiving 77373 citations.
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01 Dec 2017
TL;DR: A definition of the fractional Fourier transform on graphs (GFRFT) is proposed and consolidated, which extends the discrete fractional fourier transform (DFRFT) in the same sense the graph Fouriertransform (GFT) extended the discrete Fourier Transform (DFT).
Abstract: The emerging field of signal processing on graphs merges algebraic or spectral graph theory with discrete signal processing techniques to process signals on graphs In this paper, a definition of the fractional Fourier transform on graphs (GFRFT) is proposed and consolidated, which extends the discrete fractional Fourier transform (DFRFT) in the same sense the graph Fourier transform (GFT) extends the discrete Fourier transform (DFT) The definition is based on the eigenvalue decomposition method of defining DFRFT, for it satisfies all the agreeable properties expected of the discrete fractional Fourier transform Properties of the GFRFT are discussed, and examples of GFRFT of some graph signals are given to illustrate the transform
16 citations
TL;DR: In this article, it was shown that the spectral moment of a polymeric graph composed of n monomer units is an exact linear function of the parametern, and that this linear relation holds for all values of n, greater than a critical value ξ 0=ξ 0(k).
Abstract: It is shown that for anyk, thekth spectral moment of a polymer graph composed ofn monomer units is an exact linear function of the parametern. This linear relation holds for all values ofn, greater than a critical value ξ0=ξ0(k).
16 citations
TL;DR: It is shown that when fuzzy C-means (FCM) algorithm is used in an over-partitioning mode, the resulting membership values can be further utilized for building a connectivity graph that represents the relative distribution of the computed centroids.
16 citations
TL;DR: In this paper, the technique of describing the characteristic polynomial of a graph is extended to construction of the eigenvectors, which are expressed as linear functions of Chebyshev polynomials in order to simplify the computational effort.
Abstract: The technique of describing the characteristic polynomial of a graph is here extended to construction of the eigenvectors. Recurrence relations and path tracing are combined to generate eigenvector coefficients as polynomial functions of the eigenvalues. The polynomials are expressed as linear functions of Chebyshev polynomials in order to simplify the computational effort. Particular applications to the Huckel MO theory, including heteroatom effects, are shown.
16 citations
TL;DR: Novel graph measures based on the zeros of the characteristic polynomial by using the Randic matrix are defined and it is demonstrated that the measures encode their structural information uniquely.
16 citations