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Journal articles on the topic 'Spectral graph analysis'

Author: Grafiati

Published: 4 June 2021

Last updated: 3 February 2022

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1

Cvetkovic, Dragos. "Spectral recognition of graphs." Yugoslav Journal of Operations Research 22, no. 2 (2012): 145–61. http://dx.doi.org/10.2298/yjor120925025c.

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At some time, in the childhood of spectral graph theory, it was conjectured that non-isomorphic graphs have different spectra, i.e. that graphs are characterized by their spectra. Very quickly this conjecture was refuted and numerous examples and families of non-isomorphic graphs with the same spectrum (cospectral graphs) were found. Still some graphs are characterized by their spectra and several mathematical papers are devoted to this topic. In applications to computer sciences, spectral graph theory is considered as very strong. The benefit of using graph spectra in treating graphs is that

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Arsic, Branko, Dragos Cvetkovic, Slobodan Simic, and Milan Skaric. "Graph spectral techniques in computer sciences." Applicable Analysis and Discrete Mathematics 6, no. 1 (2012): 1–30. http://dx.doi.org/10.2298/aadm111223025a.

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We give a survey of graph spectral techniques used in computer sciences. The survey consists of a description of particular topics from the theory of graph spectra independently of the areas of Computer science in which they are used. We have described the applications of some important graph eigenvalues (spectral radius, algebraic connectivity, the least eigenvalue etc.), eigenvectors (principal eigenvector, Fiedler eigenvector and other), spectral reconstruction problems, spectra of random graphs, Hoffman polynomial, integral graphs etc. However, for each described spectral technique we indi

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Guo, Haiyan, та Bo Zhou. "On the α-spectral radius of graphs". Applicable Analysis and Discrete Mathematics, № 00 (2020): 22. http://dx.doi.org/10.2298/aadm180210022g.

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For 0 ? ? ? 1, Nikiforov proposed to study the spectral properties of the family of matrices A?(G) = ?D(G)+(1 ? ?)A(G) of a graph G, where D(G) is the degree diagonal matrix and A(G) is the adjacency matrix of G. The ?-spectral radius of G is the largest eigenvalue of A?(G). For a graph with two pendant paths at a vertex or at two adjacent vertices, we prove results concerning the behavior of the ?-spectral radius under relocation of a pendant edge in a pendant path. We give upper bounds for the ?-spectral radius for unicyclic graphs G with maximum degree ? ? 2, connected irregular graphs with

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4

Hora, Akihito. "Central Limit Theorems and Asymptotic Spectral Analysis on Large Graphs." Infinite Dimensional Analysis, Quantum Probability and Related Topics 01, no. 02 (1998): 221–46. http://dx.doi.org/10.1142/s0219025798000144.

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Regarding the adjacency matrix of a graph as a random variable in the framework of algebraic or noncommutative probability, we discuss a central limit theorem in which the size of a graph grows in several patterns. Various limit distributions are observed for some Cayley graphs and some distance-regular graphs. To obtain the central limit theorem of this type, we make combinatorial analysis of mixed moments of noncommutative random variables on one hand, and asymptotic analysis of spectral structure of the graph on the other hand.

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Coutino, Mario, Sundeep Prabhakar Chepuri, Takanori Maehara, and Geert Leus. "Fast Spectral Approximation of Structured Graphs with Applications to Graph Filtering." Algorithms 13, no. 9 (2020): 214. http://dx.doi.org/10.3390/a13090214.

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To analyze and synthesize signals on networks or graphs, Fourier theory has been extended to irregular domains, leading to a so-called graph Fourier transform. Unfortunately, different from the traditional Fourier transform, each graph exhibits a different graph Fourier transform. Therefore to analyze the graph-frequency domain properties of a graph signal, the graph Fourier modes and graph frequencies must be computed for the graph under study. Although to find these graph frequencies and modes, a computationally expensive, or even prohibitive, eigendecomposition of the graph is required, the

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6

Frangioni, Antonio, and Stefano Serra Capizzano. "Spectral Analysis of (Sequences of) Graph Matrices." SIAM Journal on Matrix Analysis and Applications 23, no. 2 (2001): 339–48. http://dx.doi.org/10.1137/s089547989935366x.

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7

Musulin, Estanislao. "Spectral Graph Analysis for Process Monitoring." Industrial & Engineering Chemistry Research 53, no. 25 (2014): 10404–16. http://dx.doi.org/10.1021/ie403966v.

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8

Alon, N., I. Dinur, E. Friedgut, and B. Sudakov. "Graph Products, Fourier Analysis and Spectral Techniques." Geometric And Functional Analysis 14, no. 5 (2004): 913–40. http://dx.doi.org/10.1007/s00039-004-0478-3.

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9

Stanković, Ljubiša, Jonatan Lerga, Danilo Mandic, Miloš Brajović, Cédric Richard, and Miloš Daković. "From Time–Frequency to Vertex–Frequency and Back." Mathematics 9, no. 12 (2021): 1407. http://dx.doi.org/10.3390/math9121407.

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The paper presents an analysis and overview of vertex–frequency analysis, an emerging area in graph signal processing. A strong formal link of this area to classical time–frequency analysis is provided. Vertex–frequency localization-based approaches to analyzing signals on the graph emerged as a response to challenges of analysis of big data on irregular domains. Graph signals are either localized in the vertex domain before the spectral analysis is performed or are localized in the spectral domain prior to the inverse graph Fourier transform is applied. The latter approach is the spectral for

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10

Sun, Miao, Elvin Isufi, Natasja M. S. de Groot, and Richard C. Hendriks. "Graph-time spectral analysis for atrial fibrillation." Biomedical Signal Processing and Control 59 (May 2020): 101915. http://dx.doi.org/10.1016/j.bspc.2020.101915.

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11

Chen, Yunxiao, Xiaoou Li, Jingchen Liu, Gongjun Xu, and Zhiliang Ying. "Exploratory Item Classification Via Spectral Graph Clustering." Applied Psychological Measurement 41, no. 8 (2017): 579–99. http://dx.doi.org/10.1177/0146621617692977.

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Large-scale assessments are supported by a large item pool. An important task in test development is to assign items into scales that measure different characteristics of individuals, and a popular approach is cluster analysis of items. Classical methods in cluster analysis, such as the hierarchical clustering, K-means method, and latent-class analysis, often induce a high computational overhead and have difficulty handling missing data, especially in the presence of high-dimensional responses. In this article, the authors propose a spectral clustering algorithm for exploratory item cluster an

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12

Yu, Guihai, Lihua Feng, Aleksandar Ilic, and Dragan Stevanovic. "The signless Laplacian spectral radius of bounded degree graphs on surfaces." Applicable Analysis and Discrete Mathematics 9, no. 2 (2015): 332–46. http://dx.doi.org/10.2298/aadm150722015y.

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Let G be an n-vertex (n ? 3) simple graph embeddable on a surface of Euler genus (the number of crosscaps plus twice the number of handles). In this paper, we present upper bounds for the signless Laplacian spectral radius of planar graphs, outerplanar graphs and Halin graphs, respectively, in terms of order and maximum degree. We also demonstrate that our bounds are sometimes better than known ones. For outerplanar graphs without internal triangles, we determine the extremal graphs with the maximum and minimum signless Laplacian spectral radii.

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13

Mezić, Igor, Vladimir A. Fonoberov, Maria Fonoberova, and Tuhin Sahai. "Spectral Complexity of Directed Graphs and Application to Structural Decomposition." Complexity 2019 (January 1, 2019): 1–18. http://dx.doi.org/10.1155/2019/9610826.

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We introduce a new measure of complexity (called spectral complexity) for directed graphs. We start with splitting of the directed graph into its recurrent and nonrecurrent parts. We define the spectral complexity metric in terms of the spectrum of the recurrence matrix (associated with the reccurent part of the graph) and the Wasserstein distance. We show that the total complexity of the graph can then be defined in terms of the spectral complexity, complexities of individual components, and edge weights. The essential property of the spectral complexity metric is that it accounts for directe

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14

Cvetkovic, Dragos, and Slobodan Simic. "Towards a spectral theory of graphs based on the signless Laplacian, III." Applicable Analysis and Discrete Mathematics 4, no. 1 (2010): 156–66. http://dx.doi.org/10.2298/aadm1000001c.

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This part of our work further extends our project of building a new spectral theory of graphs (based on the signless Laplacian) by some results on graph angles, by several comments and by a short survey of recent results.

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15

Jiang, Xinwei, Xin Song, Yongshan Zhang, Junjun Jiang, Junbin Gao, and Zhihua Cai. "Laplacian Regularized Spatial-Aware Collaborative Graph for Discriminant Analysis of Hyperspectral Imagery." Remote Sensing 11, no. 1 (2018): 29. http://dx.doi.org/10.3390/rs11010029.

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Dimensionality Reduction (DR) models are of significance to extract low-dimensional features for Hyperspectral Images (HSIs) data analysis where there exist lots of noisy and redundant spectral features. Among many DR techniques, the Graph-Embedding Discriminant Analysis framework has demonstrated its effectiveness for HSI feature reduction. Based on this framework, many representation based models are developed to learn the similarity graphs, but most of these methods ignore the spatial information, resulting in unsatisfactory performance of DR models. In this paper, we firstly propose a nove

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16

Chakrabarty, Broto, and Nita Parekh. "PRIGSA: Protein repeat identification by graph spectral analysis." Journal of Bioinformatics and Computational Biology 12, no. 06 (2014): 1442009. http://dx.doi.org/10.1142/s0219720014420098.

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Repetition of a structural motif within protein is associated with a wide range of structural and functional roles. In most cases the repeating units are well conserved at the structural level while at the sequence level, they are mostly undetectable suggesting the need for structure-based methods. Since most known methods require a training dataset, de novo approach is desirable. Here, we propose an efficient graph-based approach for detecting structural repeats in proteins. In a protein structure represented as a graph, interactions between inter- and intra-repeat units are well captured by

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17

Fokam, Rigobert, Laurent Bitjoka, and Hypolyte Egole. "Complex Basis For Spectral Analysis of Graph Signals." International Journal of Mathematics Trends and Technology 66, no. 1 (2020): 248–60. http://dx.doi.org/10.14445/22315373/ijmtt-v66i1p533.

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18

Thorne, Thomas, and Michael P. H. Stumpf. "Graph spectral analysis of protein interaction network evolution." Journal of The Royal Society Interface 9, no. 75 (2012): 2653–66. http://dx.doi.org/10.1098/rsif.2012.0220.

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We present an analysis of protein interaction network data via the comparison of models of network evolution to the observed data. We take a Bayesian approach and perform posterior density estimation using an approximate Bayesian computation with sequential Monte Carlo method. Our approach allows us to perform model selection over a selection of potential network growth models. The methodology we apply uses a distance defined in terms of graph spectra which captures the network data more naturally than previously used summary statistics such as the degree distribution. Furthermore, we include

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19

Bern, Marshall, and David Goldberg. "De Novo Analysis of Peptide Tandem Mass Spectra by Spectral Graph Partitioning." Journal of Computational Biology 13, no. 2 (2006): 364–78. http://dx.doi.org/10.1089/cmb.2006.13.364.

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20

Yurfo, Arnel M., Joel G. Adanza, and Michael Jr Patula Baldado. "On the Spectral-Equipartite Graphs and Eccentricity-Equipartite Graphs." European Journal of Pure and Applied Mathematics 14, no. 2 (2021): 358–65. http://dx.doi.org/10.29020/nybg.ejpam.v14i2.3928.

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Let G = (V, E) be a graph of order 2n. If A ⊆ V and hAi ∼= hV \Ai, then A is said to be isospectral. If for every n-element subset A of V we have hAi ∼= hV \Ai, then we say that G is spectral-equipartite. In [1], Igor Shparlinski communicated with Bibak et al., proposing a full characterization of spectral-equipartite graphs. In this paper, we gave a characterization of disconnected spectral-equipartite graphs. Moreover, we introduced the concept eccentricity-equipartite graphs.

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21

Shi, Lingsheng. "The spectral radii of a graph and its line graph." Linear Algebra and its Applications 422, no. 1 (2007): 58–66. http://dx.doi.org/10.1016/j.laa.2006.08.030.

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22

Daković, Miloš, Ljubiša Stanković, and Ervin Sejdić. "Local Smoothness of Graph Signals." Mathematical Problems in Engineering 2019 (April 8, 2019): 1–14. http://dx.doi.org/10.1155/2019/3208569.

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Analysis of vertex-varying spectral content of signals on graphs challenges the assumption of vertex invariance and requires the introduction of vertex-frequency representations as a new tool for graph signal analysis. Local smoothness, an important parameter of vertex-varying graph signals, is introduced and defined in this paper. Basic properties of this parameter are given. By using the local smoothness, an ideal vertex-frequency distribution is introduced. The local smoothness estimation is performed based on several forms of the vertex-frequency distributions, including the graph spectrog

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23

Baker, Matt, and Robert Rumely. "Harmonic Analysis on Metrized Graphs." Canadian Journal of Mathematics 59, no. 2 (2007): 225–75. http://dx.doi.org/10.4153/cjm-2007-010-2.

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24

JAFARIZADEH, M. A., and R. SUFIANI. "INVESTIGATION OF CONTINUOUS-TIME QUANTUM WALKS VIA SPECTRAL ANALYSIS AND LAPLACE TRANSFORM." International Journal of Quantum Information 05, no. 04 (2007): 575–96. http://dx.doi.org/10.1142/s0219749907003043.

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Continuous-time quantum walk (CTQW) on a given graph is investigated using the techniques of the spectral analysis and inverse Laplace transform of the Stieltjes function (Stieltjes transform of the spectral distribution) associated with the graph. It is shown that the probability amplitude of observing the CTQW at a given site at time t is related to the inverse Laplace transformation of the Stieltjes function, namely, one can calculate the probability amplitudes only by taking the inverse laplace transform of the function iGμ(is), where Gμ(x) is the Stieltjes function of the graph. The prefe

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25

Ouahada, Khmaies, and Hendrik C. Ferreira. "New Distance Concept and Graph Theory Approach for Certain Coding Techniques Design and Analysis." Communications in Applied and Industrial Mathematics 10, no. 1 (2019): 53–70. http://dx.doi.org/10.1515/caim-2019-0012.

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Abstract A New graph distance concept introduced for certain coding techniques helped in their design and analysis as in the case of distance-preserving mappings and spectral shaping codes. A graph theoretic construction, mapping binary sequences to permutation sequences and inspired from the k-cube graph has reached the upper bound on the sum of the distances for certain values of the length of the permutation sequence. The new introduced distance concept in the k-cube graph helped better understanding and analyzing for the first time the concept of distance-reducing mappings. A combination o

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26

Brinda, K. V., N. Kannan, and S. Vishveshwara. "Analysis of homodimeric protein interfaces by graph-spectral methods." Protein Engineering, Design and Selection 15, no. 4 (2002): 265–77. http://dx.doi.org/10.1093/protein/15.4.265.

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27

Hahn, Hee-Il. "Analysis of Commute Time Embedding Based on Spectral Graph." Journal of Korea Multimedia Society 17, no. 1 (2014): 34–42. http://dx.doi.org/10.9717/kmms.2014.17.1.034.

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28

Chapanond, Anurat, Mukkai S. Krishnamoorthy, and Bülent Yener. "Graph Theoretic and Spectral Analysis of Enron Email Data." Computational and Mathematical Organization Theory 11, no. 3 (2005): 265–81. http://dx.doi.org/10.1007/s10588-005-5381-4.

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29

Aizenberg, Gustavo E. "Flow graph analysis of spectral properties of multilayered media." Optical Engineering 33, no. 9 (1994): 2886. http://dx.doi.org/10.1117/12.175694.

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30

Calderara, Simone, Uri Heinemann, Andrea Prati, Rita Cucchiara, and Naftali Tishby. "Detecting anomalies in people’s trajectories using spectral graph analysis." Computer Vision and Image Understanding 115, no. 8 (2011): 1099–111. http://dx.doi.org/10.1016/j.cviu.2011.03.003.

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31

Petrovic, Miljan, Thomas A. W. Bolton, Maria Giulia Preti, Raphaël Liégeois, and Dimitri Van De Ville. "Guided graph spectral embedding: Application to the C. elegans connectome." Network Neuroscience 3, no. 3 (2019): 807–26. http://dx.doi.org/10.1162/netn_a_00084.

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Graph spectral analysis can yield meaningful embeddings of graphs by providing insight into distributed features not directly accessible in nodal domain. Recent efforts in graph signal processing have proposed new decompositions—for example, based on wavelets and Slepians—that can be applied to filter signals defined on the graph. In this work, we take inspiration from these constructions to define a new guided spectral embedding that combines maximizing energy concentration with minimizing modified embedded distance for a given importance weighting of the nodes. We show that these optimizatio

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32

Benediktovich, Vladimir I. "Spectral condition for Hamiltonicity of a graph." Linear Algebra and its Applications 494 (April 2016): 70–79. http://dx.doi.org/10.1016/j.laa.2016.01.005.

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33

Aguilar, Cesar O., Matthew Ficarra, Natalie Schurman, and Brittany Sullivan. "The role of the anti-regular graph in the spectral analysis of threshold graphs." Linear Algebra and its Applications 588 (March 2020): 210–23. http://dx.doi.org/10.1016/j.laa.2019.12.005.

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34

Huang, Hong, Zhengying Li, and Yinsong Pan. "Multi-Feature Manifold Discriminant Analysis for Hyperspectral Image Classification." Remote Sensing 11, no. 6 (2019): 651. http://dx.doi.org/10.3390/rs11060651.

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Hyperspectral image (HSI) provides both spatial structure and spectral information for classification, but many traditional methods simply concatenate spatial features and spectral features together that usually lead to the curse-of-dimensionality and unbalanced representation of different features. To address this issue, a new dimensionality reduction (DR) method, termed multi-feature manifold discriminant analysis (MFMDA), was proposed in this paper. At first, MFMDA explores local binary patterns (LBP) operator to extract textural features for encoding the spatial information in HSI. Then, u

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35

Fan, Yi-Zheng, Li Shuang-Dong, and Dong Liang. "Spectral property of certain class of graphs associated with generalized Bethe trees and transitive graphs." Applicable Analysis and Discrete Mathematics 2, no. 2 (2008): 260–75. http://dx.doi.org/10.2298/aadm0802260f.

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A generalized Bethe tree is a rooted tree for which the vertices in each level having equal degree. Let Bk be a generalized Bethe tree of k level, and let T r be a connected transitive graph on r vertices. Then we obtain a graph Bk?T r from r copies of Bk and T r by appending r roots to the vertices of T r respectively. In this paper, we give a simple way to characterize the eigenvalues of the adjacency matrix A(Bk ? T r) and the Laplacian matrix L(Bk?T r) of Bk?T r by means of symmetric tridiagonal matrices of order k. We also present some structure properties of the Perron vectors of A(Bk?T

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36

COJA-OGHLAN, AMIN, ELCHANAN MOSSEL, and DAN VILENCHIK. "A Spectral Approach to Analysing Belief Propagation for 3-Colouring." Combinatorics, Probability and Computing 18, no. 6 (2009): 881–912. http://dx.doi.org/10.1017/s096354830900981x.

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Belief propagation (BP) is a message-passing algorithm that computes the exact marginal distributions at every vertex of a graphical model without cycles. While BP is designed to work correctly on trees, it is routinely applied to general graphical models that may contain cycles, in which case neither convergence, nor correctness in the case of convergence is guaranteed. Nonetheless, BP has gained popularity as it seems to remain effective in many cases of interest, even when the underlying graph is ‘far’ from being a tree. However, the theoretical understanding of BP (and its new relative sur

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Chengcai Leng, 冷成财, 田铮 Zheng Tian, 李婧 Jing Li, and 丁明涛 Mingtao Ding. "Image registration based on matrix perturbation analysis using spectral graph." Chinese Optics Letters 7, no. 11 (2009): 996–1000. http://dx.doi.org/10.3788/col20090711.0996.

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38

Bell, Jason, and Marvin Minei. "Spectral analysis of the affine graph over the finite ring." Linear Algebra and its Applications 414, no. 1 (2006): 244–65. http://dx.doi.org/10.1016/j.laa.2005.09.020.

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39

Stevens, Jeffrey R., Ronald G. Resmini, and David W. Messinger. "Spectral-Density-Based Graph Construction Techniques for Hyperspectral Image Analysis." IEEE Transactions on Geoscience and Remote Sensing 55, no. 10 (2017): 5966–83. http://dx.doi.org/10.1109/tgrs.2017.2718547.

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40

Bernasconi, A., and B. Codenotti. "Spectral analysis of Boolean functions as a graph eigenvalue problem." IEEE Transactions on Computers 48, no. 3 (1999): 345–51. http://dx.doi.org/10.1109/12.755000.

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41

Bayram, Eda, Pascal Frossard, Elif Vural, and Aydin Alatan. "Analysis of Airborne LiDAR Point Clouds With Spectral Graph Filtering." IEEE Geoscience and Remote Sensing Letters 15, no. 8 (2018): 1284–88. http://dx.doi.org/10.1109/lgrs.2018.2834626.

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42

Xie, Fangzheng, and Yanxun Xu. "Optimal Bayesian estimation for random dot product graphs." Biometrika 107, no. 4 (2020): 875–89. http://dx.doi.org/10.1093/biomet/asaa031.

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Summary We propose and prove the optimality of a Bayesian approach for estimating the latent positions in random dot product graphs, which we call posterior spectral embedding. Unlike classical spectral-based adjacency, or Laplacian spectral embedding, posterior spectral embedding is a fully likelihood-based graph estimation method that takes advantage of the Bernoulli likelihood information of the observed adjacency matrix. We develop a minimax lower bound for estimating the latent positions, and show that posterior spectral embedding achieves this lower bound in the following two senses: it

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Zu, Baokai, Kewen Xia, Tiejun Li, et al. "SLIC Superpixel-Based l2,1-Norm Robust Principal Component Analysis for Hyperspectral Image Classification." Sensors 19, no. 3 (2019): 479. http://dx.doi.org/10.3390/s19030479.

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Hyperspectral Images (HSIs) contain enriched information due to the presence of various bands, which have gained attention for the past few decades. However, explosive growth in HSIs’ scale and dimensions causes “Curse of dimensionality” and “Hughes phenomenon”. Dimensionality reduction has become an important means to overcome the “Curse of dimensionality”. In hyperspectral images, labeled samples are more difficult to collect because they require many labor and material resources. Semi-supervised dimensionality reduction is very important in mining high-dimensional data due to the lack of co

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Oliveira, Elismar R., and Vilmar Trevisan. "Applications of rational difference equations to spectral graph theory." Journal of Difference Equations and Applications 27, no. 7 (2021): 1024–51. http://dx.doi.org/10.1080/10236198.2021.1962315.

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45

Borba, Elizandro, Eliseu Fritscher, Carlos Hoppen, and Sebastian Richter. "The p-spectral radius of the Laplacian matrix." Applicable Analysis and Discrete Mathematics 12, no. 2 (2018): 455–66. http://dx.doi.org/10.2298/aadm170206012b.

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The p-spectral radius of a graph G=(V,E) with adjacency matrix A is defined as ?(p)(G) = max||x||p=1 xT Ax. This parameter shows connections with graph invariants, and has been used to generalize some extremal problems. In this work, we define the p-spectral radius of the Laplacian matrix L as ?(p)(G) = max||x||p=1 xT Lx. We show that ?(p)(G) relates to invariants such as maximum degree and size of a maximum cut. We also show properties of ?(p)(G) as a function of p, and a upper bound on maxG: |V(G)|=n ?(p)(G) in terms of n = |V| for p > 2, which is attained if n is even.

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46

Liu, Huiqing, Mei Lu, and Feng Tian. "On the Laplacian spectral radius of a graph." Linear Algebra and its Applications 376 (January 2004): 135–41. http://dx.doi.org/10.1016/j.laa.2003.06.007.

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47

Comellas, F., and S. Gago. "Spectral bounds for the betweenness of a graph." Linear Algebra and its Applications 423, no. 1 (2007): 74–80. http://dx.doi.org/10.1016/j.laa.2006.08.027.

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48

Ghaderi, Amir Hossein, Bianca R. Baltaretu, Masood Nemati Andevari, Vishal Bharmauria, and Fuat Balci. "Synchrony and Complexity in State-Related EEG Networks: An Application of Spectral Graph Theory." Neural Computation 32, no. 12 (2020): 2422–54. http://dx.doi.org/10.1162/neco_a_01327.

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The brain may be considered as a synchronized dynamic network with several coherent dynamical units. However, concerns remain whether synchronizability is a stable state in the brain networks. If so, which index can best reveal the synchronizability in brain networks? To answer these questions, we tested the application of the spectral graph theory and the Shannon entropy as alternative approaches in neuroimaging. We specifically tested the alpha rhythm in the resting-state eye closed (rsEC) and the resting-state eye open (rsEO) conditions, a well-studied classical example of synchrony in neur

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49

Munarini, Emanuele. "Characteristic, admittance and matching polynomials of an antiregular graph." Applicable Analysis and Discrete Mathematics 3, no. 1 (2009): 157–76. http://dx.doi.org/10.2298/aadm0901157m.

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An antiregular graph is a simple graph with the maximum number of vertices with different degrees. In this paper we study the characteristic polynomial, the admittance (or Laplacian) polynomial and the matching polynomial of a connected antiregular graph. For these polynomials we obtain recurrences and explicit formulas. We also obtain some spectral properties. In particular, we prove an interlacing property for the eigenvalues and we give some bounds for the energy.

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50

SABRI, MOSTAFA. "ANDERSON LOCALIZATION FOR A MULTI-PARTICLE QUANTUM GRAPH." Reviews in Mathematical Physics 26, no. 01 (2014): 1350020. http://dx.doi.org/10.1142/s0129055x13500207.

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Abstract:

We study a multi-particle quantum graph with random potential. Taking the approach of multiscale analysis, we prove exponential and strong dynamical localization of any order in the Hilbert–Schmidt norm near the spectral edge. Apart from the results on multi-particle systems, we also prove Lifshitz-type asymptotics for single-particle systems. This shows in particular that localization for single-particle quantum graphs holds under a weaker assumption on the random potential than previously known.

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