Relevant bibliographies by topics / Graph theory

Contents

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

Academic literature on the topic 'Graph theory'

Author: Grafiati
Published: 4 June 2021
Last updated: 9 June 2025

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Journal articles on the topic "Graph theory"

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Nada A Laabi. "Subring in Graph Theory." Advances in Nonlinear Variational Inequalities 27, no. 4 (September 5, 2024): 284–87. http://dx.doi.org/10.52783/anvi.v27.1526.

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In our study, we delved into the intricacies of graph theory by exploring the properties of subrings within various types of graphs. By focusing on prime graphs and simple graphs, we unraveled the complex relationship between subring-prime graphs. Additionally, we delved into the concept of homomorphism within both simple subring graphs and prime subring graphs, adding depth to our analysis.
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Aharwal, Ramesh Prasad. "Graph Theory Applications in Machine Learning." International Journal for Research in Applied Science and Engineering Technology 13, no. 3 (March 31, 2025): 645–48. https://doi.org/10.22214/ijraset.2025.67337.

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Graph theory is the Branch of Discrete mathematics which plays a key role in Machine Learning and Data Science. Graph Theory in Machine Learning states to the application of mathematical structures known as graphs to model pairwise relations between objects in machine learning. A graph in this framework is a set of objects, called nodes, connected by links, known as edges. Each edge may be directed or undirected. In mathematics, graph theory is one of the important fields used in structural models. This paper explores the applications of Graph theory and various types of graphs in Machine Learning. The paper also discusses the advantages and various types of graph theory Algorithms which are used in Machine learning.
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ILYUTKO, DENIS PETROVICH, and VASSILY OLEGOVICH MANTUROV. "INTRODUCTION TO GRAPH-LINK THEORY." Journal of Knot Theory and Its Ramifications 18, no. 06 (June 2009): 791–823. http://dx.doi.org/10.1142/s0218216509007191.

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The present paper is an introduction to a combinatorial theory arising as a natural generalization of classical and virtual knot theory. There is a way to encode links by a class of "realizable" graphs. When passing to generic graphs with the same equivalence relations we get "graph-links". On one hand graph-links generalize the notion of virtual link, on the other hand they do not detect link mutations. We define the Jones polynomial for graph-links and prove its invariance. We also prove some a generalization of the Kauffman–Murasugi–Thistlethwaite theorem on "minimal diagrams" for graph-links.
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C.S., Harisha. "Graph Theory Approach to Number Theory Theorems." Journal of Advanced Research in Dynamical and Control Systems 12, no. 01-Special Issue (February 13, 2020): 568–72. http://dx.doi.org/10.5373/jardcs/v12sp1/20201105.

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Rohini Gore, Tejal Gore, Namrata Rokade, and Yogesh Mandlik. "“Applications of Graph Theory”." International Journal of Latest Technology in Engineering Management & Applied Science 14, no. 3 (April 4, 2025): 148–50. https://doi.org/10.51583/ijltemas.2025.140300018.

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Abstract: Graph theory is a fundamental area of mathematics with diverse applications across multiple fields. It provides a structural framework for solving complex problems by representing objects and their relationships as graphs. In computer science, graph theory is used in networking, algorithms, and artificial intelligence. It plays a crucial role in transportation and logistics, optimizing routes and traffic flow. Social networks leverage graph models for community detection and influence analysis. In biology and medicine, graph theory aids in understanding neural connections, disease spread, and genomic structures. Additionally, it is applied in cyber security, linguistics, operations research, and chemistry. The versatility of graph theory makes it an essential tool for analysing and solving real-world problems efficiently.
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Möhring, Rolf H. "Algorithmic graph theory and perfect graphs." Order 3, no. 2 (June 1986): 207–8. http://dx.doi.org/10.1007/bf00390110.

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Fujita, Takaaki. "Review of Rough Turiyam Neutrosophic Directed Graphs and Rough Pentapartitioned Neutrosophic Directed Graphs." Neutrosophic Optimization and Intelligent Systems 5 (March 4, 2025): 48–79. https://doi.org/10.61356/j.nois.2025.5500.

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Graph theory, a fundamental branch of mathematics, examines relationships between entities through the use of vertices and edges. Within this field, Uncertain Graph Theory has developed as a powerful framework to represent the uncertainties found in real world networks. Among the various uncertain graph models, Turiyam Neutrosophic Graphs and Pentapartitioned Neutrosophic Graphs are well-established. However, their extension to Directed Graphs remains relatively unexplored. To address this gap, this paper presents the concepts of the Turiyam Neutrosophic Directed Graph and the Pentapartitioned Neutrosophic Directed Graph, thereby broadening the scope of uncertain graph theory.
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Prabha, S. Celine, M. Palanivel, S. Amutha, N. Anbazhagan, Woong Cho, Hyoung-Kyu Song, Gyanendra Prasad Joshi, and Hyeonjoon Moon. "Solutions of Detour Distance Graph Equations." Sensors 22, no. 21 (November 2, 2022): 8440. http://dx.doi.org/10.3390/s22218440.

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Graph theory is a useful mathematical structure used to model pairwise relations between sensor nodes in wireless sensor networks. Graph equations are nothing but equations in which the unknown factors are graphs. Many problems and results in graph theory can be formulated in terms of graph equations. In this paper, we solved some graph equations of detour two-distance graphs, detour three-distance graphs, detour antipodal graphs involving with the line graphs.
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Bumby, Richard T., and Dana May Latch. "Categorical constructions in graph theory." International Journal of Mathematics and Mathematical Sciences 9, no. 1 (1986): 1–16. http://dx.doi.org/10.1155/s0161171286000017.

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This paper presents some graph-theoretic questions from the viewpoint of the portion of category theory which has become common knowledge. In particular, the reader is encouraged to consider whether there is only one natural category of graphs and how theories of directed graphs and undirected graphs are related.
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Fujita, Takaaki. "Claw-free Graph and AT-free Graph in Fuzzy, Neutrosophic, and Plithogenic Graphs." Information Sciences with Applications 5 (March 5, 2025): 40–55. https://doi.org/10.61356/j.iswa.2025.5502.

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Graph theory studies networks consisting of nodes (vertices) and their connections (edges), with various graph classes being extensively researched. This paper focuses on three specific graph classes: AT-Free Graphs, Claw-Free Graphs, and Triangle-Free Graphs. Additionally, it examines uncertain graph models, including Fuzzy, Intuitionistic Fuzzy, Neutrosophic, and Plithogenic Graphs, which are designed to address uncertainty in diverse applications. In this study, we introduce and analyze AT-Free Graphs, Claw-Free Graphs, and Triangle-Free Graphs within the framework of Fuzzy Graphs, investigating their properties and relationships in uncertain graph theory.
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Dissertations / Theses on the topic "Graph theory"

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Bessy, Stéphane. "Some problems in graph theory and graphs algorithmic theory." Habilitation à diriger des recherches, Université Montpellier II - Sciences et Techniques du Languedoc, 2012. http://tel.archives-ouvertes.fr/tel-00806716.

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This document is a long abstract of my research work, concerning graph theory and algorithms on graphs. It summarizes some results, gives ideas of the proof for some of them and presents the context of the different topics together with some interesting open questions connected to them The first part precises the notations used in the rest of the paper; the second part deals with some problems on cycles in digraphs; the third part is an overview of two graph coloring problems and one problem on structures in colored graphs; finally the fourth part focus on some results in algorithmic graph theory, mainly in parametrized complexity.
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Myers, Joseph Samuel. "Extremal theory of graph minors and directed graphs." Thesis, University of Cambridge, 2003. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.619614.

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Johnson, Chase R. "Molecular Graph Theory." Digital WPI, 2010. https://digitalcommons.wpi.edu/etd-theses/1179.

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Graph Theory is a branch of mathematics that has a wealth of applications to other science and engineering disciplines, specifically Chemistry. The primary application of graphs to Chemistry is related to understanding of structure and symmetry at the molecular level. By projecting a molecule to the plane and examining it as a graph, a lot can be learned about the underlying molecular structure of a given compound. Using concepts of Graph Theory this masters project examines the underlying structures of two specific families of compounds, fullerenes and zeolites, from a chemical and mathematical perspective.
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Feghali, Carl. "Topics in graph colouring and extremal graph theory." Thesis, Durham University, 2016. http://etheses.dur.ac.uk/11790/.

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In this thesis we consider three problems related to colourings of graphs and one problem in extremal graph theory. Let $G$ be a connected graph with $n$ vertices and maximum degree $\Delta(G)$. Let $R_k(G)$ denote the graph with vertex set all proper $k$-colourings of $G$ and two $k$-colourings are joined by an edge if they differ on the colour of exactly one vertex. Our first main result states that $R_{\Delta(G)+1}(G)$ has a unique non-trivial component with diameter $O(n^2)$. This result can be viewed as a reconfigurations analogue of Brooks' Theorem and completes the study of reconfigurations of colourings of graphs with bounded maximum degree. A Kempe change is the operation of swapping some colours $a$, $b$ of a component of the subgraph induced by vertices with colour $a$ or $b$. Two colourings are Kempe equivalent if one can be obtained from the other by a sequence of Kempe changes. Our second main result states that all $\Delta(G)$-colourings of a graph $G$ are Kempe equivalent unless $G$ is the complete graph or the triangular prism. This settles a conjecture of Mohar (2007). Motivated by finding an algorithmic version of a structure theorem for bull-free graphs due to Chudnovsky (2012), we consider the computational complexity of deciding if the vertices of a graph can be partitioned into two parts such that one part is triangle-free and the other part is a collection of complete graphs. We show that this problem is NP-complete when restricted to five classes of graphs (including bull-free graphs) while polynomial-time solvable for the class of cographs. Finally we consider a graph-theoretic version formulated by Holroyd, Spencer and Talbot (2007) of the famous Erd\H{o}s-Ko-Rado Theorem in extremal combinatorics and obtain some results for the class of trees.
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Nikwigize, Adolphe. "Graph theory : Route problems." Thesis, Linnéuniversitetet, Institutionen för datavetenskap, fysik och matematik, DFM, 2012. http://urn.kb.se/resolve?urn=urn:nbn:se:lnu:diva-17397.

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Berg, Deborah. "Connections Between Voting Theory and Graph Theory." Scholarship @ Claremont, 2005. https://scholarship.claremont.edu/hmc_theses/178.

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Mathematical concepts have aided the progression of many different fields of study. Math is not only helpful in science and engineering, but also in the humanities and social sciences. Therefore, it seemed quite natural to apply my preliminary work with set intersections to voting theory, and that application has helped to focus my thesis. Rather than studying set intersections in general, I am attempting to study set intersections and what they mean in a voting situation. This can lead to better ways to model preferences and to predict which campaign platforms will be most popular. Because I feel that allowing people to only vote for one candidate results in a loss of too much information, I consider approval voting, where people can vote for as many platforms as they like.
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Hatt, Justin Dale. "Online assessment of graph theory." Thesis, Brunel University, 2016. http://bura.brunel.ac.uk/handle/2438/13389.

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The objective of this thesis is to establish whether or not online, objective questions in elementary graph theory can be written in a way that exploits the medium of computer-aided assessment. This required the identification and resolution of question design and programming issues. The resulting questions were trialled to give an extensive set of answer files which were analysed to identify whether computer delivery affected the questions in any adverse ways and, if so, to identify practical ways round these issues. A library of questions spanning commonly-taught topics in elementary graph theory has been designed, programmed and added to the graph theory topic within an online assessment and learning tool used at Brunel University called Mathletics. Distracters coded into the questions are based on errors students are likely to make, partially evidenced by final examination scripts. Questions were provided to students in Discrete Mathematics modules with an extensive collection of results compiled for analysis. Questions designed for use in practice environments were trialled on students from 2007 – 2008 and then from 2008 to 2014 inclusive under separate testing conditions. Particular focus is made on the relationship of facility and discrimination between comparable questions during this period. Data is grouped between topic and also year group for the 2008 – 2014 tests, namely 2008 to 2011 and 2011 to 2014, so that it may then be determined what factors, if any, had an effect on the overall results for these questions. Based on the analyses performed, it may be concluded that although CAA questions provide students with a means for improving their learning in this field of mathematics, what makes a question more challenging is not solely based on the number of ways a student can work out his/her solution but also on several other factors that depend on the topic itself.
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Keevash, Peter. "Topics in extremal graph theory." Thesis, University of Cambridge, 2003. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.619938.

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Law, Ka-ho, and 羅家豪. "Some results in graph theory." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2010. http://hub.hku.hk/bib/B44899816.

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Morrison, Julie Lindsay. "Computational graph theory in bioinformatics." Thesis, University of Strathclyde, 2006. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.435114.

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Books on the topic "Graph theory"

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Golumbic, Martin Charles. Algorithmic graph theory and perfect graphs. 2nd ed. Amsterdam: North Holland, 2004.

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Bondy, J. A. Graph theory. New York: Springer, 2010.

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Gould, Ronald. Graph theory. Menlo Park, Calif: Benjamin/Cummings Pub. Co., 1988.

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Gera, Ralucca, Stephen Hedetniemi, and Craig Larson, eds. Graph Theory. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-31940-7.

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Bondy, J. A., and U. S. R. Murty. Graph Theory. London: Springer London, 2008. http://dx.doi.org/10.1007/978-1-84628-970-5.

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Diestel, Reinhard. Graph Theory. Berlin, Heidelberg: Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-14279-6.

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Gera, Ralucca, Teresa W. Haynes, and Stephen T. Hedetniemi, eds. Graph Theory. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-97686-0.

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Diestel, Reinhard. Graph Theory. Berlin, Heidelberg: Springer Berlin Heidelberg, 2017. http://dx.doi.org/10.1007/978-3-662-53622-3.

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Merris, Russell. Graph Theory. Hoboken, NJ, USA: John Wiley & Sons, Inc., 2000. http://dx.doi.org/10.1002/9781118033043.

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Saoub, Karin R. Graph Theory. Boca Raton: CRC Press, 2021. | Series: Textbooks in mathematics: Chapman and Hall/CRC, 2021. http://dx.doi.org/10.1201/9781138361416.

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Book chapters on the topic "Graph theory"

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Xu, Jin. "Graph Theory Fundamentals." In Maximal Planar Graph Theory and the Four-Color Conjecture, 1–35. Singapore: Springer Nature Singapore, 2025. https://doi.org/10.1007/978-981-96-4745-3_1.

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Abstract In this section, we will discuss some of the basic terminologies and concepts of graph theory, which will be assumed throughout the rest of this book, together with a few fundamental properties that characterize planar graphs, e.g., the well-known Kuratowski Theorem and planarity testing algorithm, etc.
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O’Regan, Gerard. "Graph Theory." In Texts in Computer Science, 141–53. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-44561-8_9.

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Kirwan, Brock, and Ty Bodily. "Graph Theory." In Encyclopedia of Clinical Neuropsychology, 1607–8. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-57111-9_9069.

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Sucar, Luis Enrique. "Graph Theory." In Probabilistic Graphical Models, 27–38. London: Springer London, 2015. http://dx.doi.org/10.1007/978-1-4471-6699-3_3.

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Harris, John M., Jeffry L. Hirst, and Michael J. Mossinghoff. "Graph Theory." In Combinatorics and Graph Theory, 1–127. New York, NY: Springer New York, 2008. http://dx.doi.org/10.1007/978-0-387-79711-3_1.

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Neri, Ferrante. "Graph Theory." In Linear Algebra for Computational Sciences and Engineering, 363–430. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-40341-0_11.

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O’Regan, Gerard. "Graph Theory." In Mathematics in Computing, 267–75. London: Springer London, 2012. http://dx.doi.org/10.1007/978-1-4471-4534-9_16.

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Kirwan, Brock, and Ty Bodily. "Graph Theory." In Encyclopedia of Clinical Neuropsychology, 1–2. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-56782-2_9069-1.

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Wallis, W. D. "Graph Theory." In A Beginner’s Guide to Finite Mathematics, 137–86. Boston, MA: Birkhäuser Boston, 2004. http://dx.doi.org/10.1007/978-1-4757-3814-8_4.

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Wallis, W. D. "Graph Theory." In A Beginner’s Guide to Discrete Mathematics, 205–49. Boston, MA: Birkhäuser Boston, 2003. http://dx.doi.org/10.1007/978-1-4757-3826-1_7.

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Conference papers on the topic "Graph theory"

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Bao, Jueming, Zhaorong Fu, Tanumoy Pramanik, Jun Mao, Yulin Chi, Yingkang Cao, Chonghao Zhai, et al. "Multiphoton Multidimensional Entanglement Based on Graph Theory." In CLEO: Applications and Technology, JTu2A.224. Washington, D.C.: Optica Publishing Group, 2024. http://dx.doi.org/10.1364/cleo_at.2024.jtu2a.224.

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We demonstrate the capability of graph theory scheme to realize complex multiphoton multidimensional state. We show the generation of quantum states based on graph theory was realized by the reconfigurable integrated quantum chip. The 4-photon 3-dimensional GHZ state was generated and verified and manipulated for the first time.
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Zhang, Jun, and Ziping Zhao. "Improved Stability Bounds for Graph Convolutional Neural Networks Under Graph Perturbations." In 2024 IEEE Information Theory Workshop (ITW), 307–12. IEEE, 2024. https://doi.org/10.1109/itw61385.2024.10806975.

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Nomura, Saki, Junya Hara, Hiroshi Higashi, and Yuichi Tanaka. "Dynamic Sensor Placement on Graphs Based on Graph Signal Sampling Theory." In 2024 Asia Pacific Signal and Information Processing Association Annual Summit and Conference (APSIPA ASC), 1–6. IEEE, 2024. https://doi.org/10.1109/apsipaasc63619.2025.10848795.

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Lopez, Blake R., and Victor M. Zavala. "Analysis of Chemical Engineering Curricula Using Graph Theory." In Foundations of Computer-Aided Process Design, 975–82. Hamilton, Canada: PSE Press, 2024. http://dx.doi.org/10.69997/sct.190804.

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Chemical engineering is a highly complex interconnected major. Just as chemical engineers have broken complex processes into unit operations, the chemical engineering curriculum has been broken up into courses. The organization of these courses vary among institutions and are based on years of prior teachings and research. Despite this, there have been calls to revaluate the curriculum from both industry and academia. We propose a graph-based representation of curricula in which topics are represented by nodes and topic dependencies are represented by directed edges forming a directed acyclic graph. This enables using graph theory measures and tools to provide formal ways of evaluating a curriculum. Additionally, the abstraction is readily understandable meaning conversations between instructors regarding the curriculum can occur within a department and even across institutions. This abstraction is explained with a simplified curriculum and applied to the undergraduate chemical engineering curriculum at University of Wisconsin-Madison. Highly and lowly connected topics are identified and approaches for grouping the topics into modules are discussed.
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Freeman, Jason. "Graph theory." In ACM SIGGRAPH 2008 art gallery. New York, New York, USA: ACM Press, 2008. http://dx.doi.org/10.1145/1400385.1400449.

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Freeman, Jason. "Graph theory." In the 6th ACM SIGCHI conference. New York, New York, USA: ACM Press, 2007. http://dx.doi.org/10.1145/1254960.1254998.

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Freeman, Jason. "Graph theory." In the 7th international conference. New York, New York, USA: ACM Press, 2007. http://dx.doi.org/10.1145/1279740.1279794.

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Oliveira, Daniel, Carlos Magno Abreu, Eduardo Ogasawara, Eduardo Bezerra, and Leonardo De Lima. "A Science Gateway to Support Research in Spectral Graph Theory." In XXXIV Simpósio Brasileiro de Banco de Dados. Sociedade Brasileira de Computação - SBC, 2019. http://dx.doi.org/10.5753/sbbd.2019.8826.

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Describing classes of graphs that optimize a function of the eigenvalues subject to some constraints is one of the topics addressed by Spectral Graph Theory (SGT). In this paper, we propose RioGraphX, a science gateway developed on top of Apache Spark, which aims to obtain all graphs that optimize a given mathematical function of the eigenvalues of a graph. Initial experiments involving small graphs have pointed out optimal graphs in a reasonable computational time, and also have shown that leveraging parallel processing is a promising approach to handle larger graphs.
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Devi, M. Manjula, and K. Karuppasamy. "Application of graph theory in chemical graphs." In INTELLIGENT BIOTECHNOLOGIES OF NATURAL AND SYNTHETIC BIOLOGICALLY ACTIVE SUBSTANCES: XIV Narochanskie Readings. AIP Publishing, 2023. http://dx.doi.org/10.1063/5.0179080.

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THOMASSEN, CARSTEN. "CHROMATIC GRAPH THEORY." In Proceedings of the International Conference on Fundamental Sciences: Mathematics and Theoretical Physics. WORLD SCIENTIFIC, 2001. http://dx.doi.org/10.1142/9789812811264_0008.

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Reports on the topic "Graph theory"

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Burch, Kimberly Jordan. Chemical Graph Theory. Washington, DC: The MAA Mathematical Sciences Digital Library, August 2008. http://dx.doi.org/10.4169/loci002857.

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GEORGIA INST OF TECH ATLANTA. Graph Minors: Structure Theory and Algorithms. Fort Belvoir, VA: Defense Technical Information Center, April 1993. http://dx.doi.org/10.21236/ada266033.

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Thomas, Robin. Graph Minors: Structure Theory and Algorithms. Fort Belvoir, VA: Defense Technical Information Center, January 1993. http://dx.doi.org/10.21236/ada271851.

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Obert, James, Sean D. Turner, and Jason Hamlet. Graph Theory and IC Component Design Analysis. Office of Scientific and Technical Information (OSTI), March 2020. http://dx.doi.org/10.2172/1606298.

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

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Shukla, Dr Minal. Exploring Graph Theory to Enhance Performance of Blockchain. ResearchHub Technologies, Inc., June 2024. http://dx.doi.org/10.55277/researchhub.w5pebey6.

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Shukla, Dr Minal. Integrating Graph Theory for Consensus Mechanism of Blockchain Technology. ResearchHub Technologies, Inc., July 2024. http://dx.doi.org/10.55277/researchhub.l34eqdoa.

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Mesbahi, Mehran. Dynamic Security and Robustness of Networked Systems: Random Graphs, Algebraic Graph Theory, and Control over Networks. Fort Belvoir, VA: Defense Technical Information Center, February 2012. http://dx.doi.org/10.21236/ada567125.

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Hrebeniuk, Bohdan V. Modification of the analytical gamma-algorithm for the flat layout of the graph. [б. в.], December 2018. http://dx.doi.org/10.31812/123456789/2882.

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The planarity of graphs is one of the key sections of graph theory. Although a graph is an abstract mathematical object, most often it is graph visualization that makes it easier to study or develop in a particular area, for example, the infrastructure of a city, a company’s management or a website’s web page. In general, in the form of a graph, it is possible to depict any structures that have connections between the elements. But often such structures grow to such dimensions that it is difficult to determine whether it is possible to represent them on a plane without intersecting the bonds. There are many algorithms that solve this issue. One of these is the gamma method. The article identifies its problems and suggests methods for solving them, and also examines ways to achieve them.
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