Relevant bibliographies by topics / Graph spectrum

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Graph spectrum'

Author: Grafiati
Published: 4 June 2021
Last updated: 1 February 2022

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Journal articles on the topic "Graph spectrum"

1

Alhevaz, Abdollah, Maryam Baghipur, Hilal A. Ganie, and Yilun Shang. "The Generalized Distance Spectrum of the Join of Graphs." Symmetry 12, no. 1 (2020): 169. http://dx.doi.org/10.3390/sym12010169.

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Let G be a simple connected graph. In this paper, we study the spectral properties of the generalized distance matrix of graphs, the convex combination of the symmetric distance matrix D ( G ) and diagonal matrix of the vertex transmissions T r ( G ) . We determine the spectrum of the join of two graphs and of the join of a regular graph with another graph, which is the union of two different regular graphs. Moreover, thanks to the symmetry of the matrices involved, we study the generalized distance spectrum of the graphs obtained by generalization of the join graph operation through their eig
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Li, Shuchao, and Shujing Wang. "The $A_{\alpha}$- spectrum of graph product." Electronic Journal of Linear Algebra 35 (February 1, 2019): 473–81. http://dx.doi.org/10.13001/1081-3810.3857.

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Let $A(G)$ and $D(G)$ denote the adjacency matrix and the diagonal matrix of vertex degrees of $G$, respectively. Define $$ A_{\alpha}(G)=\alpha D(G)+(1-\alpha)A(G) $$ for any real $\alpha\in [0,1]$. The collection of eigenvalues of $A_{\alpha}(G)$ together with multiplicities is called the $A_{\alpha}$-\emph{spectrum} of $G$. Let $G\square H$, $G[H]$, $G\times H$ and $G\oplus H$ be the Cartesian product, lexicographic product, directed product and strong product of graphs $G$ and $H$, respectively. In this paper, a complete characterization of the $A_{\alpha}$-spectrum of $G\square H$ for arb
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Yu, Guidong, Tao Yu, Xiangwei Xia, and Huan Xu. "Spectral Sufficient Conditions on Pancyclic Graphs." Complexity 2021 (July 15, 2021): 1–8. http://dx.doi.org/10.1155/2021/3630245.

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A pancyclic graph of order n is a graph with cycles of all possible lengths from 3 to n . In fact, it is NP-complete that deciding whether a graph is pancyclic. Because the spectrum of graphs is convenient to be calculated, in this study, we try to use the spectral theory of graphs to study this problem and give some sufficient conditions for a graph to be pancyclic in terms of the spectral radius and the signless Laplacian spectral radius of the graph.
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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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RAJASEKARAN, SANGUTHEVAR, and VAMSI KUNDETI. "SPECTRUM BASED TECHNIQUES FOR GRAPH ISOMORPHISM." International Journal of Foundations of Computer Science 20, no. 03 (2009): 479–99. http://dx.doi.org/10.1142/s0129054109006693.

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The graph isomorphism problem is to check if two given graphs are isomorphic. Graph isomorphism is a well studied problem and numerous algorithms are available for its solution. In this paper we present algorithms for graph isomorphism that employ the spectra of graphs. An open problem that has fascinated many a scientist is if there exists a polynomial time algorithm for graph isomorphism. Though we do not solve this problem in this paper, the algorithms we present take polynomial time. These algorithms have been tested on a good collection of instances. However, we have not been able to prov
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Adiga, Chandrashekar, Kinkar Das, and B. R. Rakshith. "Some Graphs Determined by their Signless Laplacian (Distance) Spectra." Electronic Journal of Linear Algebra 36, no. 36 (2020): 461–72. http://dx.doi.org/10.13001/ela.2020.4951.

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In literature, there are some results known about spectral determination of graphs with many edges. In [M.~C\'{a}mara and W.H.~Haemers. Spectral characterizations of almost complete graphs. {\em Discrete Appl. Math.}, 176:19--23, 2014.], C\'amara and Haemers studied complete graph with some edges deleted for spectral determination. In fact, they found that if the deleted edges form a matching, a complete graph $K_m$ provided $m \le n-2$, or a complete bipartite graph, then it is determined by its adjacency spectrum. In this paper, the graph $K_{n}\backslash K_{l,m}$ $(n>l+m)$ which is obtai
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Liu, Yu, and Lihua You. "Further Results on the Nullity of Signed Graphs." Journal of Applied Mathematics 2014 (2014): 1–8. http://dx.doi.org/10.1155/2014/483735.

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The nullity of a graph is the multiplicity of the eigenvalue zero in its spectrum. A signed graph is a graph with a sign attached to each of its edges. In this paper, we apply the coefficient theorem on the characteristic polynomial of a signed graph and give two formulae on the nullity of signed graphs with cut-points. As applications of the above results, we investigate the nullity of the bicyclic signed graphΓ∞p,q,l, obtain the nullity set of unbalanced bicyclic signed graphs, and thus determine the nullity set of bicyclic signed graphs.
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Iranmanesh, Mohammad, and Mahboubeh Saheli. "Toward a Laplacian spectral determination of signed ∞-graphs." Filomat 32, no. 6 (2018): 2283–94. http://dx.doi.org/10.2298/fil1806283i.

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A signed graph consists of a (simple) graph G=(V,E) together with a function ? : E ? {+,-} called signature. Matrices can be associated to signed graphs and the question whether a signed graph is determined by the set of its eigenvalues has gathered the attention of several researchers. In this paper we study the spectral determination with respect to the Laplacian spectrum of signed ?-graphs. After computing some spectral invariants and obtain some constraints on the cospectral mates, we obtain some non isomorphic signed graphs cospectral to signed ?-graphs and we study the spectral character
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Sciriha, Irene. "Joining Forces for Reconstruction Inverse Problems." Symmetry 13, no. 9 (2021): 1687. http://dx.doi.org/10.3390/sym13091687.

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A spectral inverse problem concerns the reconstruction of parameters of a parent graph from prescribed spectral data of subgraphs. Also referred to as the P–NP Isomorphism Problem, Reconstruction or Exact Graph Matching, the aim is to seek sets of parameters to determine a graph uniquely. Other related inverse problems, including the Polynomial Reconstruction Problem (PRP), involve the recovery of graph invariants. The PRP seeks to extract the spectrum of a graph from the deck of cards each showing the spectrum of a vertex-deleted subgraph. We show how various algebraic methods join forces to
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Urakawa, Hajime. "The Spectrum of an Infinite Graph." Canadian Journal of Mathematics 52, no. 5 (2000): 1057–84. http://dx.doi.org/10.4153/cjm-2000-044-2.

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AbstractIn this paper, we consider the (essential) spectrum of the discrete Laplacian of an infinite graph. We introduce a new quantity for an infinite graph, in terms of which we give new lower bound estimates of the (essential) spectrum and give also upper bound estimates when the infinite graph is bipartite. We give sharp estimates of the (essential) spectrum for several examples of infinite graphs.
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Dissertations / Theses on the topic "Graph spectrum"

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Ghenciu, Eugen Andrei. "Dimension spectrum and graph directed Markov systems." Thesis, University of North Texas, 2006. https://digital.library.unt.edu/ark:/67531/metadc5226/.

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In this dissertation we study graph directed Markov systems (GDMS) and limit sets associated with these systems. Given a GDMS S, by the Hausdorff dimension spectrum of S we mean the set of all positive real numbers which are the Hausdorff dimension of the limit set generated by a subsystem of S. We say that S has full Hausdorff dimension spectrum (full HD spectrum), if the dimension spectrum is the interval [0, h], where h is the Hausdorff dimension of the limit set of S. We give necessary conditions for a finitely primitive conformal GDMS to have full HD spectrum. A GDMS is said to be regular
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Glover, Cory. "The Non-Backtracking Spectrum of a Graph and Non-Bactracking PageRank." BYU ScholarsArchive, 2021. https://scholarsarchive.byu.edu/etd/9194.

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This thesis studies two problems centered around non-backtracking walks on graphs. First, we analyze the spectrum of the non-backtracking matrix of a graph. We show how to obtain the eigenvectors of the non-backtracking matrix using a smaller matrix and in doing so, create a block diagonal decomposition which more clearly expresses the non-backtracking matrix eigenvalues. Additionally, we develop upper and lower bounds on the matrix spectrum and use the spectrum to investigate properties of the graph. Second, we investigate the difference between PageRank and non-backtracking PageRank. We show
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Rittenhouse, Michelle L. "Properties and Recent Applications in Spectral Graph Theory." VCU Scholars Compass, 2008. http://scholarscompass.vcu.edu/etd/1126.

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There are numerous applications of mathematics, specifically spectral graph theory, within the sciences and many other fields. This paper is an exploration of recent applications of spectral graph theory, including the fields of chemistry, biology, and graph coloring. Topics such as the isomers of alkanes, the importance of eigenvalues in protein structures, and the aid that the spectra of a graph provides when coloring a graph are covered, as well as others.The key definitions and properties of graph theory are introduced. Important aspects of graphs, such as the walks and the adjacency ma
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Swami, Sameer. "Graph theoretic approach to QoS guaranteed spectrum allocation in cognitive radio networks." Cincinnati, Ohio : University of Cincinnati, 2008. http://rave.ohiolink.edu/etdc/view.cgi?acc_num=ucin1223916863.

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Thesis (M.S.)--University of Cincinnati, 2008.<br>Advisor: Kenneth Berman. Title from electronic thesis title page (viewed Feb.16, 2008). Includes abstract. Keywords: Cognitive radios; channel allocation; greedy priority optimization Includes bibliographical references.
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Black, Chelsea Lynn. "Resting-State Functional Brain Networks in Bipolar Spectrum Disorder: A Graph Theoretical Investigation." Diss., Temple University Libraries, 2016. http://cdm16002.contentdm.oclc.org/cdm/ref/collection/p245801coll10/id/393135.

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Psychology<br>Ph.D.<br>Neurobiological theories of bipolar spectrum disorder (BSD) propose that the emotional dysregulation characteristic of BSD stems from disrupted prefrontal control over subcortical limbic structures (Strakowski et al., 2012; Depue & Iacono, 1989). However, existing neuroimaging research on functional connectivity between frontal and limbic brain regions remains inconclusive, and is unable to adequately characterize global functional network dynamics. Graph theoretical analysis provides a framework for understanding the local and global connections of the brain and compari
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Schumacher, R. "Improving the capacity of radio spectrum : exploration of the acyclic orientations of a graph." Thesis, City, University of London, 2017. http://openaccess.city.ac.uk/17910/.

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The efficient use of radio spectrum depends upon frequency assignment within a telecommunications network. The solution space of the frequency assignment problem is best described by the acyclic orientations of the network. An acyclic orientation Ɵ of a graph (network) G is an orientation of the edges of the graph which does not create any directed cycles. We are primarily interested in how many ways this is possible for a given graph, which is the count of the number of acyclic orientations, a(G). This is just the evaluation of the chromatic polynomial of the graph χ(G; λ) at λ = -1. Calculat
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Sinop, Ali Kemal. "Graph Partitioning and Semi-definite Programming Hierarchies." Research Showcase @ CMU, 2012. http://repository.cmu.edu/dissertations/145.

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Graph partitioning is a fundamental optimization problem that has been intensively studied. Many graph partitioning formulations are important as building blocks for divide-and-conquer algorithms on graphs as well as to many applications such as VLSI layout, packet routing in distributed networks, clustering and image segmentation. Unfortunately such problems are notorious for the huge gap between known best known approximation algorithms and hardness of approximation results. In this thesis, we study approximation algorithms for graph partitioning problems using a strong hierarchy of relaxati
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Shah, Vijay K. "A DIVERSE BAND-AWARE DYNAMIC SPECTRUM ACCESS ARCHITECTURE FOR CONNECTIVITY IN RURAL COMMUNITIES." UKnowledge, 2019. https://uknowledge.uky.edu/cs_etds/82.

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Ubiquitous connectivity plays an important role in improving the quality of life in terms of economic development, health and well being, social justice and equity, as well as in providing new educational opportunities. However, rural communities which account for 46% of the world's population lacks access to proper connectivity to avail such societal benefits, creating a huge "digital divide" between the urban and rural areas. A primary reason is that the Information and Communication Technologies (ICT) providers have less incentives to invest in rural areas due to lack of promising revenue r
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Medrano, Archie T. "Super-Euclidean graphs and super-Heisenberg graphs : their spectral and graph-theoretic properties /." Diss., Connect to a 24 p. preview or request complete full text in PDF format. Access restricted to UC campuses, 1998. http://wwwlib.umi.com/cr/ucsd/fullcit?p9901440.

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Goch, Caspar Jonas [Verfasser], та Uwe [Akademischer Betreuer] Oelfke. "Expanding Graph Theoretical Indices to Include Medical Knowledge - An Assessment of Classification Accuracy in the Case of Autism Spectrum Disorders / Caspar Jonas Goch ; Betreuer: Uwe Oelfke". Heidelberg : Universitätsbibliothek Heidelberg, 2014. http://d-nb.info/1179925386/34.

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Books on the topic "Graph spectrum"

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Spectral graph theory. Published for the Conference Board of the mathematical sciences by the American Mathematical Society, 1997.

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Cvetković, Dragoš M. Applications of graph spectra. Edited by Gutman Ivan 1947-. Matematički institut SANU, 2009.

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Puppe, Thomas. Spectral Graph Drawing: A Survey. VDM Verlag Dr. Mu ller Aktiengesellschaft & Co. KG, 2008.

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Graph spectra for complex networks. Cambridge University Press, 2011.

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Al-Doujan, Fawwaz Awwad. Spectra of graphs. University of East Anglia, 1992.

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H, Haemers Willem, and SpringerLink (Online service), eds. Spectra of Graphs. Andries E. Brouwer and Willem H. Haemers, 2012.

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Brouwer, Andries E., and Willem H. Haemers. Spectra of Graphs. Springer New York, 2012. http://dx.doi.org/10.1007/978-1-4614-1939-6.

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Spectral analysis on graph-like spaces. Springer-Verlag, 2012.

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Post, Olaf. Spectral Analysis on Graph-like Spaces. Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-23840-6.

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Cvetković, Dragoš M. Eigenspaces of graphs. Cambridge University Press, 1997.

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Book chapters on the topic "Graph spectrum"

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Brouwer, Andries E., and Willem H. Haemers. "Graph Spectrum." In Universitext. Springer New York, 2011. http://dx.doi.org/10.1007/978-1-4614-1939-6_1.

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Liu, Hongjuan, and Lidong Wang. "Completing the Spectrum for a Class of Graph Designs." In Communications in Computer and Information Science. Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-25002-6_3.

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Baird, Paul. "The Geometric Spectrum of a Graph and Associated Curvatures." In Modern Approaches to Discrete Curvature. Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-58002-9_7.

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Zhang, Li, Cunqian Yu, and Rongxi He. "Time-Aware Routing and Spectrum Assignment Assisted by 3D-Spectrum Auxiliary Graph in Elastic Optical Networks." In Lecture Notes in Electrical Engineering. Springer Singapore, 2019. http://dx.doi.org/10.1007/978-981-13-6508-9_49.

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He, Qing. "A New Model of Spectrum Allocation Based on the Graph Theory." In Recent Advances in Computer Science and Information Engineering. Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-25769-8_94.

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Lu, Xiaomin, Haowen Yan, and Zhonghui Wang. "On the graph-spectrum of spatial direction relationships between object groups." In Advances in Energy Science and Equipment Engineering II. CRC Press, 2017. http://dx.doi.org/10.1201/9781315116167-73.

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Li, Feng, Lili Yang, Jiangxin Zhang, and Li Wang. "A Novel Spectrum Allocation Scheme in Femtocell Networks Using Improved Graph Theory." In Machine Learning and Intelligent Communications. Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-030-00557-3_18.

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Morris, Carrie, and Islem Rekik. "Autism Spectrum Disorder Diagnosis Using Sparse Graph Embedding of Morphological Brain Networks." In Graphs in Biomedical Image Analysis, Computational Anatomy and Imaging Genetics. Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-67675-3_2.

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Tolan, Ertan, and Zerrin Isik. "Graph Theory Based Classification of Brain Connectivity Network for Autism Spectrum Disorder." In Bioinformatics and Biomedical Engineering. Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-78723-7_45.

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Kimoto, Kazufumi. "Generalized Group–Subgroup Pair Graphs." In International Symposium on Mathematics, Quantum Theory, and Cryptography. Springer Singapore, 2020. http://dx.doi.org/10.1007/978-981-15-5191-8_14.

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Abstract A regular finite graph is called a Ramanujan graph if its zeta function satisfies an analog of the Riemann Hypothesis. Such a graph has a small second eigenvalue so that it is used to construct cryptographic hash functions. Typically, explicit family of Ramanujan graphs are constructed by using Cayley graphs. In the paper, we introduce a generalization of Cayley graphs called generalized group–subgroup pair graphs, which are a generalization of group–subgroup pair graphs defined by Reyes-Bustos. We study basic properties, especially spectra of them.
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Conference papers on the topic "Graph spectrum"

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Yang, Mu, and Choon Yik Tang. "Distributed estimation of graph spectrum." In 2015 American Control Conference (ACC). IEEE, 2015. http://dx.doi.org/10.1109/acc.2015.7171143.

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Dianjie Lu, Jing Lu, and Xiaoxia Huang. "Clustering based spectrum allocation scheme using spectral graph partitioning." In 2010 2nd International Asia Conference on Informatics in Control, Automation and Robotics (CAR 2010). IEEE, 2010. http://dx.doi.org/10.1109/car.2010.5456599.

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Chepuri, Sundeep Prabhakar, and Geert Leus. "Subsampling for graph power spectrum estimation." In 2016 IEEE Sensor Array and Multichannel Signal Processing Workshop (SAM). IEEE, 2016. http://dx.doi.org/10.1109/sam.2016.7569707.

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Li, Yanhua, and Zhi-Li Zhang. "Understanding Complex Networks Using Graph Spectrum." In WWW '15: 24th International World Wide Web Conference. ACM, 2015. http://dx.doi.org/10.1145/2740908.2744718.

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Cohen-Steiner, David, Weihao Kong, Christian Sohler, and Gregory Valiant. "Approximating the Spectrum of a Graph." In KDD '18: The 24th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining. ACM, 2018. http://dx.doi.org/10.1145/3219819.3220119.

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Tran, Trong Nhan, and Airlie Chapman. "Generalized Graph Product: Spectrum, Trajectories and Controllability." In 2018 IEEE Conference on Decision and Control (CDC). IEEE, 2018. http://dx.doi.org/10.1109/cdc.2018.8618713.

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Guo, Linqi, Changhong Zhao, and Steven H. Low. "Graph Laplacian Spectrum and Primary Frequency Regulation." In 2018 IEEE Conference on Decision and Control (CDC). IEEE, 2018. http://dx.doi.org/10.1109/cdc.2018.8619252.

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Niepert, Mathias, and Alberto Garcia-Duran. "TOWARDS A SPECTRUM OF GRAPH CONVOLUTIONAL NETWORKS." In 2018 IEEE Data Science Workshop (DSW). IEEE, 2018. http://dx.doi.org/10.1109/dsw.2018.8439903.

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Xiao, Shuang, Wenzao Li, Lingling Yang, and Zhan Wen. "Graph-Coloring Based Spectrum Sharing for V2V communication." In 2020 International Conference on UK-China Emerging Technologies (UCET). IEEE, 2020. http://dx.doi.org/10.1109/ucet51115.2020.9205455.

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Zhang, Jing, and Rangachar Kasturi. "Text Detection Using Edge Gradient and Graph Spectrum." In 2010 20th International Conference on Pattern Recognition (ICPR). IEEE, 2010. http://dx.doi.org/10.1109/icpr.2010.968.

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Reports on the topic "Graph spectrum"

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Guattery, Stephen, and Gary L. Miller. On the Performance of Spectral Graph Partitioning Methods. Defense Technical Information Center, 1994. http://dx.doi.org/10.21236/ada292214.

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Sweeney, Matthew, and Emily Shinkle. Understanding Discrete Fracture Networks Through Spectral Graph Theory. Office of Scientific and Technical Information (OSTI), 2021. http://dx.doi.org/10.2172/1812641.

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Sweeney, Matthew, and Emily Shinkle. Understanding Discrete Fracture Networks Through Spectral Graph Theory. Office of Scientific and Technical Information (OSTI), 2021. http://dx.doi.org/10.2172/1812622.

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Hendrickson, B., and R. Leland. An improved spectral graph partitioning algorithm for mapping parallel computations. Office of Scientific and Technical Information (OSTI), 1992. http://dx.doi.org/10.2172/6970738.

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