Relevant bibliographies by topics / Geometric and topological aspects of graph theory

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

Academic literature on the topic 'Geometric and topological aspects of graph theory'

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Published: 4 June 2021
Last updated: 14 February 2022

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Journal articles on the topic "Geometric and topological aspects of graph theory"

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Asif, Muhammad, Hamad Almohamedh, Muhammad Hussain, Khalid M. Alhamed, Abdulrazaq A. Almutairi, and Sultan Almotairi. "An Approach to the Geometric-Arithmetic Index for Graphs under Transformations’ Fact over Pendent Paths." Complexity 2021 (June 24, 2021): 1–13. http://dx.doi.org/10.1155/2021/3745862.

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Graph theory is a dynamic tool for designing and modeling of an interconnection system by a graph. The vertices of such graph are processor nodes and edges are the connections between these processors nodes. The topology of a system decides its best use. Geometric-arithmetic index is one of the most studied graph invariant to characterize the topological aspects of underlying interconnection networks or graphs. Transformation over graph is also an important tool to define new network of their own choice in computer science. In this work, we discuss transformed family of graphs. Let Γ n k , l be the connected graph comprises by k number of pendent path attached with fully connected vertices of the n-vertex connected graph Γ . Let A α Γ n k , l and A α β Γ n k , l be the transformed graphs under the fact of transformations A α and A α β , 0 ≤ α ≤ l , 0 ≤ β ≤ k − 1 , respectively. In this work, we obtained new inequalities for the graph family Γ n k , l and transformed graphs A α Γ n k , l and A α β Γ n k , l which involve GA Γ . The presence of GA Γ makes the inequalities more general than all those which were previously defined for the GA index. Furthermore, we characterize extremal graphs which make the inequalities tight.
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Islam, Tanweer Ul, Zeeshan Saleem Mufti, Aqsa Ameen, Muhammad Nauman Aslam, and Ali Tabraiz. "On Certain Aspects of Topological Indices." Journal of Mathematics 2021 (May 3, 2021): 1–20. http://dx.doi.org/10.1155/2021/9913529.

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A topological index, also known as connectivity index, is a molecular structure descriptor calculated from a molecular graph of a chemical compound which characterizes its topology. Various topological indices are categorized based on their degree, distance, and spectrum. In this study, we calculated and analyzed the degree-based topological indices such as first general Zagreb index M r G , geometric arithmetic index GA G , harmonic index H G , general version of harmonic index H r G , sum connectivity index λ G , general sum connectivity index λ r G , forgotten topological index F G , and many more for the Robertson apex graph. Additionally, we calculated the newly developed topological indices such as the AG 2 G and Sanskruti index for the Robertson apex graph G.
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Saeed, Nouman, Kai Long, Tanweer Ul Islam, Zeeshan Saleem Mufti, and Ayesha Abbas. "Topological Study of Zeolite Socony Mobil-5 via Degree-Based Topological Indices." Journal of Chemistry 2021 (June 23, 2021): 1–13. http://dx.doi.org/10.1155/2021/5522800.

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Graph theory is a subdivision of discrete mathematics. In graph theory, a graph is made up of vertices connected through edges. Topological indices are numerical parameters or descriptors of graph. Topological index tells the symmetry of compound and helps us to compare those mathematical values, with boiling point, melting point, density, viscosity, hydrophobic surface area, polarity, etc., of that compound. In the present research paper, degree-based topological indices of Zeolite Socony Mobil-5 are calculated. Names of those topological indices are Randić index, first Zagreb index, general sum connectivity index, hyper-Zagreb index, geometric index, ABC index, etc.
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Bokhary, Syed Ahtsham Ul Haq, Muhammad Imran, and Sadia Manzoor. "On molecular topological properties of dendrimers." Canadian Journal of Chemistry 94, no. 2 (February 2016): 120–25. http://dx.doi.org/10.1139/cjc-2015-0466.

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Topological indices are numerical parameters of a graph that characterize its topology and are usually graph invariant. In a QSAR/QSPR study, physicochemical properties and topological indices such as the Randić, atom–bond connectivity (ABC), and geometric–arithmetic (GA) indices are used to predict the bioactivity of different chemical compounds. Graph theory has found a considerable use in this area of research. In this paper, we study the degree-based molecular topological indices such as ABC4 and GA5 for certain families of dendrimers. We derive the analytical closed formulae for these classes of dendrimers.
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Manjunath, Muddalapuram, V. Lokesha, Suvarna, and Sushmitha Jain. "Bounds for the Topological Indices of ℘ graph." European Journal of Pure and Applied Mathematics 14, no. 2 (May 18, 2021): 340–50. http://dx.doi.org/10.29020/nybg.ejpam.v14i2.3715.

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Topological indices are mathematical measure which correlates to the chemical structures of any simple finite graph. These are used for Quantitative Structure-Activity Relationship (QSAR) and Quantitative Structure-Property Relationship (QSPR). In this paper, we define operator graph namely, ℘ graph and structured properties. Also, establish the lower and upper bounds for few topological indices namely, Inverse sum indeg index, Geometric-Arithmetic index, Atom-bond connectivity index, first zagreb index and first reformulated Zagreb index of ℘-graph.
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Imran, Muhammad, Muhammad Siddiqui, Amna Abunamous, Dana Adi, Saida Rafique, and Abdul Baig. "Eccentricity Based Topological Indices of an Oxide Network." Mathematics 6, no. 7 (July 18, 2018): 126. http://dx.doi.org/10.3390/math6070126.

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Graph theory has much great advances in the field of mathematical chemistry. Chemical graph theory has become very popular among researchers because of its wide applications in mathematical chemistry. The molecular topological descriptors are the numerical invariants of a molecular graph and are very useful for predicting their bioactivity. A great variety of such indices are studied and used in theoretical chemistry, pharmaceutical researchers, in drugs and in different other fields. In this article, we study the chemical graph of an oxide network and compute the total eccentricity, average eccentricity, eccentricity based Zagreb indices, atom-bond connectivity (ABC) index and geometric arithmetic index of an oxide network. Furthermore, we give analytically closed formulas of these indices which are helpful in studying the underlying topologies.
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Idrees, Nazeran, Muhammad Jawwad Saif, Afshan Sadiq, Asia Rauf, and Fida Hussain. "Topological Indices of H-Naphtalenic Nanosheet." Open Chemistry 16, no. 1 (November 14, 2018): 1184–88. http://dx.doi.org/10.1515/chem-2018-0131.

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AbstractIn chemical graph theory, a single numeric number related to a chemical structure is called a topological descriptor or topological index of a graph. In this paper, we compute analytically certain topological indices for H-Naphtalenic nanosheet like Randic index, first Zagreb index, second Zagreb index, geometric arithmetic index, atom bond connectivity index, sum connectivity index and hyper-Zagreb index using edge partition technique. The first multiple Zagreb index and the second multiple Zagreb index of the nanosheet are also discussed in this paper.
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Bača, Martin, Jarmila Horváthová, Martina Mokrišová, Andrea Semaničová-Feňovčíková, and Alžbeta Suhányiová. "On topological indices of a carbon nanotube network." Canadian Journal of Chemistry 93, no. 10 (October 2015): 1157–60. http://dx.doi.org/10.1139/cjc-2015-0175.

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A numerical quantity that characterizes the whole structure of a graph is called a topological index. The concept of Randić (Rα), atom−bond connectivity (ABC), and geometric−arithmetic (GA) topological indices was established in chemical graph theory based on vertex degrees. In this paper, we study a carbon nanotube network that is motivated by the molecular structure of a regular hexagonal lattice and determine Rα, ABC, and GA indices for this important class of networks.
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Bojarski, B., and G. Khimshiashvili. "Global Geometric Aspects of Riemann–Hilbert Problems." gmj 8, no. 4 (December 2001): 713–26. http://dx.doi.org/10.1515/gmj.2001.713.

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Abstract We discuss some global properties of an abstract geometric model for Riemann–Hilbert problems introduced by the first author. In particular, we compute the homotopy groups of elliptic Riemann–Hilbert problems and describe some connections with the theory of Fredholm structures which enable one to introduce more subtle geometrical and topological invariants for families of such problems.
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Liu, Jia-Bao, Imran Khalid, Mohammad Tariq Rahim, Masood Ur Rehman, Faisal Ali, and Muhammad Salman. "Eccentric topological properties of a graph associated to a finite dimensional vector space." Main Group Metal Chemistry 43, no. 1 (October 6, 2020): 164–76. http://dx.doi.org/10.1515/mgmc-2020-0020.

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AbstractA topological index is actually designed by transforming a chemical structure into a number. Topological index is a graph invariant which characterizes the topology of the graph and remains invariant under graph automorphism. Eccentricity based topological indices are of great importance and play a vital role in chemical graph theory. In this article, we consider a graph (non-zero component graph) associated to a finite dimensional vector space over a finite filed in the context of the following eleven eccentricity based topological indices: total eccentricity index; average eccentricity index; eccentric connectivity index; eccentric distance sum index; adjacent distance sum index; connective eccentricity index; geometric arithmetic index; atom bond connectivity index; and three versions of Zagreb indices. Relationship of the investigated indices and their dependency with respect to the involved parameters are also visualized by evaluating them numerically and by plotting their results.
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Dissertations / Theses on the topic "Geometric and topological aspects of graph theory"

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Loeb, Sarah. "Extending List Colorings of Planar Graphs." Scholarship @ Claremont, 2011. http://scholarship.claremont.edu/hmc_theses/6.

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In the study of list colorings of graphs, we assume each vertex of a graph has a specified list of colors from which it may be colored. For planar graphs, it is known that there is a coloring for any list assignment where each list contains five colors. If we have some vertices that are precolored, can we extend this to a coloring of the entire graph? We explore distance constraints when we allow the lists to contain an extra color. For lists of length five, we fix $W$ as a subset of $V(G)$ such that all vertices in $W$ have been assigned colors from their respective lists. We give a new, simplified proof where there are a small number of precolored vertices on the same face. We also explore cases where $W=\{u,v\}$ and $G$ has a separating $C_3$ or $C_4$ between $u$ and $v$.
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Weinstein, Madeleine. "Adinkras and Arithmetical Graphs." Scholarship @ Claremont, 2016. http://scholarship.claremont.edu/hmc_theses/85.

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Adinkras and arithmetical graphs have divergent origins. In the spirit of Feynman diagrams, adinkras encode representations of supersymmetry algebras as graphs with additional structures. Arithmetical graphs, on the other hand, arise in algebraic geometry, and give an arithmetical structure to a graph. In this thesis, we will interpret adinkras as arithmetical graphs and see what can be learned. Our work consists of three main strands. First, we investigate arithmetical structures on the underlying graph of an adinkra in the specific case where the underlying graph is a hypercube. We classify all such arithmetical structures and compute some of the corresponding volumes and linear ranks. Second, we consider the case of a reduced arithmetical graph structure on the hypercube and explore the wealth of relationships that exist between its linear rank and several notions of genus that appear in the literature on graph theory and adinkras. Third, we study modifications of the definition of an arithmetical graph that incorporate some of the properties of an adinkra, such as the vertex height assignment or the edge dashing. To this end, we introduce the directed arithmetical graph and the dashed arithmetical graph. We then explore properties of these modifications in an attempt to see if our definitions make sense, answering questions such as whether the volume is still an integer and whether there are still only finitely many arithmetical structures on a given graph.
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Vaz, Alves Gleifer. "Transformations for proof-graphs with cycle treatment augmented via geometric perspective techniques." Universidade Federal de Pernambuco, 2009. https://repositorio.ufpe.br/handle/123456789/1418.

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O presente trabalho é baseada em dois aspectos fundamentais: (i) o estudo de procedimentos de normalização para sistemas de provas, especialmente para a lógica clássica com dedução natural; e (ii) a investigação de técnicas da perspectiva geométrica aplicadas em propriedades da teoria da prova. Com isso, a motivação específica deste trabalho reside principalmente na análise daqueles trabalhos que estão voltados à definição de técnicas da normalização através de mecanismos da perspectiva geométrica. Destaca-se que técnicas da perspectiva geométrica trazem o uso de arcabouços gráficos e/ou topológicos com a finalidade de representar sistemas formais de provas e suas propriedades. Dessa forma, a primeira parte do documento apresenta o uso de técnicas e arcabouços topológicos para estabelecer algumas propriedades, como, por exemplo, o critério de corretude e a normalização de sistemas de prova. Ao passo que a segunda parte do documento é inicialmente direcionada à descrição de algumas abordagens de normalização (principalmente) para a lógica clássica com dedução natural. E o complemento da segunda parte é dedicado à definição do principal objetivo do trabalho, i.e., desenvolver um procedimento de normalização para o conjunto completo de operadores dos N-Grafos, através do auxílio de algumas técnicas de perspectiva geométrica. (Destaca-se que as técnicas de perspectiva geométrica, aplicadas à normalização dos N-Grafos, não fazem uso de arcabouços topológicos). N-Grafos é um sistema de prova com múltipla conclusão definido para lógica clássica proposicional com dedução natural. Ademais, os N-Grafos possuem tanto regras lógicas como estruturais, estruturas cíclicas são permitidas e além disso as derivações são representadas como grafos direcionados. De fato, a princpal característica do procedimento de normalização aqui apresentado é fornecer um tratamento completo para as estruturas cíclicas. Ou seja, são definidas classes de ciclos válidos, critério de corretude, propriedades e ainda um algoritmo específico para normalizar os ciclos nos N-Grafos. Destaca-se que esses elementos são construídos através do auxílio de arcabouços gráficos. Além disso, o mecanismo de normalização é capaz de lidar com os diferentes papéis executados pelos operadores ?/>. Adicionalmente, apresenta-se uma prova direta da normalização fraca para os N-Grafos, bem como, a determinação das propriedades da subfórmula e da separação
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Garcia, Cantu Ros Anselmo. "Thermodynamic and kinetic aspects of interaction networks." Doctoral thesis, Universite Libre de Bruxelles, 2007. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/210420.

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In view of the fact that a same complex phenomenon can be approached by different conceptual frameworks, it is natural to inquire on the possibility to find connections between different types of quantities, such as topological, dynamical, statistical or thermodynamical, characterizing the same system. The present work is built on the idea that this line of approach can provide interesting insights on possible universal principles governing complex phenomena. In Chapter I we introduce concepts and tools of dynamical systems and thermodynamics as applied in macroscopic scale description as well as, for a later use, a number of selected representative models. In Chapter II we briefly present the elements of the theory of Markov processes describing a large class of stochastic process and also introduce some important concepts on the probabilistic description of deterministic systems. This chapter ends with a thermodynamic formulation accounting for the evolution of the entropy under the effect of stochastic fluctuations. In Chapter III, after introducing the main concepts and recent advances in network theory, we provide a connection between dynamical systems and network theory, which shows how universal structural properties of evolving networks can arise from deterministic dynamics. More specifically, we show explicitly the relation between the connectivity patterns of these networks and the indicators of the underlying dynamics, such as the local Lyapunov exponents. Our analysis is applied to representative models of chaotic maps, chaotic flows and is finally extended to stochastic processes. In Chapter IV we address the inverse problem, namely, processes whose dynamics is determined, in part, by the structure of the network in which they are embedded. In particular, we focus on systems of particles diffusing on a lattice and reacting instantaneously upon encountering each other. We study the role of the topology, the degree of synchronicity of motion and the reaction mechanism on the efficiency of the process. This lead us to identify a common generic mechanism responsible for the behavior of the efficiency, as a function of the control parameters. Finally, in Chapter V we study the connection between the topology and the thermodynamic properties of reaction networks, with focus on the entropy production and the system’s efficiency at nonequilibrium steady states. We also explore the connection between dynamic and thermodynamic properties of nonlinear feedbacks, as well as the response properties of reaction networks against both deterministic and stochastic external perturbations. We address networks of varying topologies, from regular lattices to complex structures./Le présent travail s’inscrit dans le domaine de recherche sur les systèmes complexes. Différentes approches, basées des systèmes dynamiques, de la thermodynamique des systèmes hors d’équilibre, de la physique statistique et, plus récemment, de la théorie des réseaux, sont combinés afin d’explorer des liens entre différentes types de grandeurs qui caractérisent certaines classes de comportements complexes. Dans le Chapitre I nous introduisons les principaux concepts et outils de systèmes dynamiques et de thermodynamique. Dans le Chapitre II nous présentons premièrement des éléments de la théorie de processus de Markov, ainsi que les concepts à la base de la description probabiliste des systèmes déterministes. Nous finissons le chapitre en proposant une formulation thermodynamique qui décrit l’évolution de l’entropie hors d’équilibre, soumis à l’influence de fluctuations stochastiques. Dans le Chapitre III nous introduisons les concepts de base en théorie des réseaux, ainsi qu’un résumé générale des progrès récents dans le domaine. Nous établissons ensuite une connexion entre la théorie des systèmes dynamiques et la théorie de réseaux. Celle-ci permet d’approfondir la compréhension des mécanismes responsables de l’émergence des propriétés structurelles dans des réseaux crées par des lois dynamiques déterministes. En particulier, nous mettons en évidence la relation entre des motifs de connectivité de ce type de réseaux et des indicateurs de la dynamique sous-jacente, tel que des exposant de Lyapounov locaux. Notre analyse est illustrée par des applications et des flots chaotiques et étendue à des processus stochastiques. Dans le Chapitre IV nous étudions le problème complémentaire, à savoir, celui de processus dont la dynamique est déterminée, en partie, par la structure du réseau dans lequel elle se déroule. Plus précisément, nous nous concentrons sur le cas de systèmes de particules réactives, diffusent au travers d’un réseau et réagissant instantanément lorsqu’un rencontre se produit entre elles. Nous étudions le rôle de la topologie, du degré de synchronicité des mouvements et aussi celui du mécanisme de réaction sur l’efficacité du processus. Dans les différents modèles étudiés, nous identifions un mécanisme générique commun, responsable du comportement de l’efficacité comme fonction des paramètres de contrôle. Enfin, dans le Chapitre V nous abordons la connexion entre la topologie et les propriétés thermodynamiques des réseaux de réactions, en analysant le comportement local et global de la production d’entropie et l’efficacité du système dans des état stationnaires de non-équilibre. Nous explorons aussi la connexion entre la dynamique et les propriétés de boucles de rétroaction non linéaires, ainsi que les propriétés de réponse des réseaux de réaction à des perturbations stochastiques et déterministes externes. Nous considérons le cas de réseaux à caractère régulier aussi bien que celui de réseaux complexes.


Doctorat en Sciences
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Bellet, Thomas. "Transformations de graphes pour la modélisation géométrique à base topologique." Thesis, Poitiers, 2012. http://www.theses.fr/2012POIT2261/document.

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De nombreux domaines comme le jeu vidéo, l’architecture, l’ingénierie ou l’archéologie font désormais appel à la modélisation géométrique. Les objets à représenter sont de natures diverses, et leurs opérations de manipulation sont spécifiques. Ainsi, les modeleurs sont nombreux car tous spécialisés à leur domaine d’application. Or ils sont à la fois chers à développer, souvent peu robustes, et difficilement extensibles. Nous avons proposé dans la thèse l’approche alternative suivante :– fournir un langage dédié à la modélisation qui permet de définir les opérations quelque soit le domaine d’application ; dans ce langage, les objets sont représentés avec le modèle topologique des cartes généralisées, dont nous avons étendu la définition aux plongements ; les opérations sont elles définies par des règles de transformation de graphes, issues de la théorie des catégorie ;– garantir les opérations définies dans le langage à l’aide de conditions de cohérence ; une opération dont la définition vérifie ces conditions ne produit pas d’anomalie ;– développer un noyau de modeleur générique qui interprète ce langage ; les opérations définies sont directement appliquées dans le modeleur, sans implantation dans un langage de programmation ; l’outil assure également la vérification automatique des conditions du langage pour prévenir un utilisateur lorsqu’il propose une opération incohérente.Le langage et le modeleur développés se sont révélés performants à la fois en termes de temps de développement et en termes de temps machine. L’implantation d’une nouvelle opération par une règle ne prend que quelques minutes à l’aide des conditions du langage, au contraire de l’approche classi
Geometric modeling is now involved in many fields such as: video games, architecture, engineering and archaeology. The represented objects are very different from one field to another, and so are their modeling operations. Furthermore, many specific types of modeling software are designed for high programing costs, but with a relatively low rate of effectiveness.The following is an alternative approach:– we have conceived a dedicated language for geometric modeling that will allow us to define any operation of any field; objects in this language are defined with the topological model of generalized maps, this definition has been extended to the embedding informations; here the operations are defined as graph transformation rules which originate from the category theory;– we have ensured operation definitions with consistency conditions; these operations that satisfy those conditions do not generate anomalies; – we have designed generic modeling software to serve as an interpreter of this language; the operation definitions are directly applied without the need for more programing; the software also automatically checks the language conditions and warns the user if he designs a non-consistent operation.The provided language and software prove to be efficient, and all for a low programing cost. Designing a new operation takes only minutes thanks to the language conditions, as opposed to hours of programming and debugging with the past approach
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Kappos, Elias. "lp-Kohomologie, insbesondere Verschwindungssätze für lp-Kohomologie." Doctoral thesis, 2007. http://hdl.handle.net/11858/00-1735-0000-0006-B392-6.

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Books on the topic "Geometric and topological aspects of graph theory"

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Sunada, Toshikazu. Topological Crystallography: With a View Towards Discrete Geometric Analysis. Tokyo: Springer Japan, 2013.

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Carlson, Jon F., Srikanth B. Iyengar, and Julia Pevtsova, eds. Geometric and Topological Aspects of the Representation Theory of Finite Groups. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-94033-5.

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Barg, Alexander, and O. R. Musin. Discrete geometry and algebraic combinatorics. Providence, Rhode Island: American Mathematical Society, 2014.

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Topology and geometry in dimension three: Triangulations, invariants, and geometric structures : conference in honor of William Jaco's 70th birthday, June 4-6, 2010, Oklahoma State University, Stillwater, OK. Providence, R.I: American Mathematical Society, 2011.

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author, Rosen Daniel 1980, ed. Function theory on symplectic manifolds. Providence, Rhode Island, USA: American Mathematical Society, 2014.

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Koli︠a︡da, S. F. Dynamics and numbers: A special program, June 1-July 31, 2014, Max Planck Institute for Mathematics, Bonn, Germany : international conference, July 21-25, 2014, Max Planck Institute for Mathematics, Bonn, Germany. Edited by Max-Planck-Institut für Mathematik. Providence, Rhode Island: American Mathematical Society, 2016.

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Tao, Terence. Hilbert's fifth problem and related topics. Providence, Rhode Island: American Mathematical Society, 2014.

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Schurz, Henri, Philip J. Feinsilver, Gregory Budzban, and Harry Randolph Hughes. Probability on algebraic and geometric structures: International research conference in honor of Philip Feinsilver, Salah-Eldin A. Mohammed, and Arunava Mukherjea, June 5-7, 2014, Southern Illinois University, Carbondale, Illinois. Edited by Mohammed Salah-Eldin 1946- and Mukherjea Arunava 1941-. Providence, Rhode Island: American Mathematical Society, 2016.

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Jaco, William H., Hyam Rubinstein, Craig David Hodgson, Martin Scharlemann, and Stephan Tillmann. Geometry and topology down under: A conference in honour of Hyam Rubinstein, July 11-22, 2011, The University of Melbourne, Parkville, Australia. Providence, Rhode Island: American Mathematical Society, 2013.

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Vladas, Sidoravicius, and Smirnov S. (Stanislav) 1970-, eds. Probability and statistical physics in St. Petersburg: St. Petersburg School in Probability and Statistical Physics : June 18-29, 2012 : St. Petersburg State University, St. Petersburg, Russia. Providence, Rhode Island: American Mathematical Society, 2015.

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Book chapters on the topic "Geometric and topological aspects of graph theory"

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Buzaglo, Sarit, Rom Pinchasi, and Günter Rote. "Topological Hypergraphs." In Thirty Essays on Geometric Graph Theory, 71–81. New York, NY: Springer New York, 2012. http://dx.doi.org/10.1007/978-1-4614-0110-0_6.

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Camacho, César, and Alcides Lins Neto. "Topological Aspects of the Theory of Group Actions." In Geometric Theory of Foliations, 159–74. Boston, MA: Birkhäuser Boston, 1985. http://dx.doi.org/10.1007/978-1-4612-5292-4_9.

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Avramov, Luchezar L., and Srikanth B. Iyengar. "Restricting Homology to Hypersurfaces." In Geometric and Topological Aspects of the Representation Theory of Finite Groups, 1–23. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-94033-5_1.

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Henke, Ellen, and Justin Lynd. "Extensions of the Benson-Solomon Fusion Systems." In Geometric and Topological Aspects of the Representation Theory of Finite Groups, 251–68. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-94033-5_10.

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Mathew, Akhil. "Examples of Descent up to Nilpotence." In Geometric and Topological Aspects of the Representation Theory of Finite Groups, 269–311. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-94033-5_11.

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Garibaldi, Skip, Robert M. Guralnick, and Daniel K. Nakano. "Globally Irreducible Weyl Modules for Quantum Groups." In Geometric and Topological Aspects of the Representation Theory of Finite Groups, 313–26. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-94033-5_12.

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Oliver, B. "A Remark on the Construction of Centric Linking Systems." In Geometric and Topological Aspects of the Representation Theory of Finite Groups, 327–37. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-94033-5_13.

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Pevtsova, Julia, and Jim Stark. "Varieties of Elementary Subalgebras of Maximal Dimension for Modular Lie Algebras." In Geometric and Topological Aspects of the Representation Theory of Finite Groups, 339–75. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-94033-5_14.

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Sobaje, Paul. "Varieties Related to the Problem of Lifting $$G_r$$-Modules to G." In Geometric and Topological Aspects of the Representation Theory of Finite Groups, 377–92. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-94033-5_15.

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Stevenson, Greg. "Complete Boolean Algebras are Bousfield Lattices." In Geometric and Topological Aspects of the Representation Theory of Finite Groups, 393–405. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-94033-5_16.

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Conference papers on the topic "Geometric and topological aspects of graph theory"

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Hedberg, Thomas D., Allison Barnard Feeney, and Vijay Srinivasan. "On Practice and Theory of Constructive Composite Geometry and Topology." In ASME 2019 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2019. http://dx.doi.org/10.1115/detc2019-97134.

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Abstract This paper synthesizes a theory from industrial best practices codified in recent standards. Recent editions of ASME and ISO standards codify the evolving industrial best practices in defining and modeling the information about products made from fibrous composite materials. A theory of constructive composite geometry and topology is synthesized from these practices. Major features of this theory include (1) a constructive composite geometry tree that is equivalent to the ply/laminate tables of the standards, (2) an adjacency graph that captures a crucial aspect of the topology of the geometric cell complex structure of composite products, and (3) conformal mapping of ply surfaces using rosettes in the lay-up process. It also addresses the geometrical and topological structure of fiber arrangements inside the plies. The goal of the theory is to provide a scientific basis for standards that enable the digital transformation of composite product manufacturing.
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Sengupta, Ambar N. "Gauge theory in two dimensions: Topological, geometric and probabilistic aspects." In Proceedings of a Satellite Conference of ICM 2006. WORLD SCIENTIFIC, 2007. http://dx.doi.org/10.1142/9789812791559_0008.

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Slavutin, Michael, Offer Shai, and Andreas Müller. "Mobility Determination of Mechanisms Based on Rigidity Theory." In ASME 2012 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/detc2012-71289.

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Rigidity theory deals mostly with the topological computation in mechanical systems, i.e. it aims at making generic statements. Mechanism theory is mainly concerned with the geometrical analysis but again also with generic statements. Even more so for mobility analysis where one is interested in both the generic mobility and that of a particular mechanism. In rigidity theory the mathematical foundation is the topology representation using bar-joint and body-bar graphs, and the corresponding rigidity matrix. In this paper novel geometric rules for constructing the body-bar rigidity matrix are derived for general planar mechanisms comprising revolute and prismatic joints. This allows, for the first time, the treatment of general planar mechanisms with the body-bar approach. The rigidity matrix is also derived for spatial mechanisms with spherical joints. The bar-joint rigidity matrix is shown to be a special case of body-bar representation. It is shown that the rigidity matrices allow for mobility calculation as shown in the paper. This paper is aimed at supplying a unified view and as a result to enable the mechanisms community to employ the theorems and methods used in rigidity theory. An algorithm for mobility determination — the pebble game — is discussed. This algorithm always finds the correct generic mobility if the mechanism can be represented by a body-bar graph.
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Khristodulo, Olga, Vladimir Gvozdev, Oxana Bezhaeva, and Marat Shamsutdinov. "Assessment of the characteristics of the municipal solid waste management system based on the apparatus of the theory of reliability." In International Conference "Computing for Physics and Technology - CPT2020". Bryansk State Technical University, 2020. http://dx.doi.org/10.30987/conferencearticle_5fce277281cca9.86270786.

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Currently, the problem of organizing a municipal solid waste management system (MSW) has become more acute in Russian regions and all over the world. Various environmental and economic problems, as well as problems related to public health negatively affect many aspects of the development of modern society. Therefore, the careful organization of the management of the MSW management system is of great social importance and needs constant improvement. In this paper, we look at the MSW management system from the point of various scientific approaches, namely, structural analysis methods, geoinformation technology methods, reliability theory for complex technical systems, evergetics, graph theory and fuzzy logic methods, including the apparatus of linguistic variables. The purpose of the work is to show the possibility of application and systematic combination of the above scientific methods that have proven themselves well in their fields to a new area of the MSW management systems. However, just application of these approaches is impossible without their further adaptation and systematization from the point of view of existing approaches to the management of similar systems. As part of this study, elements of the MSW management system were identified and a topological model of the system was developed. Structural-logical models of reliability at various levels of abstraction were also built.
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Hahn, Elad, and Offer Shai. "The Unique Engineering Properties of Assur Groups/Graphs, Assur Kinematic Chains, Baranov Trusses and Parallel Robots." In ASME 2016 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2016. http://dx.doi.org/10.1115/detc2016-59135.

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Modular topological structures, commonly known as Assur groups, have been an important subject of research in machine theory over the past several decades. In this paper, some unique engineering properties which appear in this type of structures and only in them are exposed. The concept of Assur groups is reformulated in terms of graphs and named Assur Graphs (AGs). The graph representation enables to present the inter-connectivity between all the elements of the AG, which is the fundamental characteristic from which all its unique properties derive. This inter-connectivity leads to unique properties in three main engineering aspects of structures: kinematics, statics and singularity positions. These properties can be exploited for better analysis and synthesis of structures such as mechanisms, robots and trusses.
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