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Relevant bibliographies by topics / Graph theory. Categories (Mathematics)

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Academic literature on the topic 'Graph theory. Categories (Mathematics)'

Author: Grafiati

Published: 4 June 2021

Last updated: 13 February 2022

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Journal articles on the topic "Graph theory. Categories (Mathematics)"

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Medová, Páleníková, Rybanský, and Naštická. "Undergraduate Students’ Solutions of Modeling Problems in Algorithmic Graph Theory." Mathematics 7, no. 7 (June 26, 2019): 572. http://dx.doi.org/10.3390/math7070572.

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Graphs can be considered as useful mathematical models. Graph algorithms are a common part of undergraduate courses in discrete mathematics. Even though they have been successfully implemented in secondary curricula, little research has been dedicated to the analysis of students’ work. Within a discrete mathematics course for university students, several graph algorithms were introduced via their applications. At the end of the course, the students took a test focused, inter alia, on applications of the algorithms. The mistakes that occurred in 127 students’ solutions of three problems (the Chinese postman problem, the shortest path problem, and the minimum spanning tree problem) were categorized and compared. Surprisingly, no mistakes were identified in the mathematization of situations or in the interpretation of results with respect to the wording of the problem. The categories of errors varied regardless of the problem types. Hierarchical cluster analysis grouped together the students’ solutions for the Chinese postman problem and the minimum spanning tree problem. By means of nonparametric item response theory analysis, the Chinese postman problem was identified as the most problematic for students. Possible sources of this difficulty are discussed in more detail herein.

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Grossman, Stuart C. "On graph theoretical SAR and the mathematical theory of categories." Journal of Molecular Structure: THEOCHEM 233 (September 1991): 21–34. http://dx.doi.org/10.1016/0166-1280(91)85051-8.

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Derksen, Harm. "The Graph Isomorphism Problem and approximate categories." Journal of Symbolic Computation 59 (December 2013): 81–112. http://dx.doi.org/10.1016/j.jsc.2013.06.002.

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Phoa, Wesley. "Building domains from graph models." Mathematical Structures in Computer Science 2, no. 3 (September 1992): 277–99. http://dx.doi.org/10.1017/s0960129500001481.

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In this paper we study partial equivalence relations (PERs) over graph models of the λcalculus. We define categories of PERs that behave like predomains, and like domains. These categories are small and complete; so we can solve domain equations and construct polymorphic types inside them. Upper, lower and convex powerdomain constructions are also available, as well as interpretations of subtyping and bounded quantification. Rather than performing explicit calculations with PERs, we work inside the appropriate realizability topos: this is a model of constructive set theory in which PERs, can be regarded simply as special kinds of sets. In this framework, most of the definitions and proofs become quite smple and attractives. They illustrative some general technicques in ‘synthetic domain theory’ that rely heavily on category theory; using these methods, we can obtain quite powerful results about classes of PERs, even when we know very little about their internal structure.

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BRUGGINK, H. J. SANDER, and BARBARA KÖNIG. "Recognizable languages of arrows and cospans." Mathematical Structures in Computer Science 28, no. 8 (August 8, 2018): 1290–332. http://dx.doi.org/10.1017/s096012951800018x.

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In this article, we generalize Courcelle's recognizable graph languages and results on monadic second-order logic to more general structures.First, we give a category-theoretical characterization of recognizability. A recognizable subset of arrows in a category is defined via a functor into the category of relations on finite sets. This can be seen as a straightforward generalization of finite automata. We show that our notion corresponds to recognizable graph languages if we apply the theory to the category of cospans of graphs.In the second part of the paper, we introduce a simple logic that allows to quantify over the subobjects of a categorical object. Again, we show that, for the category of graphs, this logic is equally expressive as monadic second-order graph logic (msogl). Furthermore, we show that in the more general setting of hereditary pushout categories, a class of categories closely related to adhesive categories, we can recover Courcelle's result that everymsogl-expressible property is recognizable. This is done by giving an inductive translation of formulas of our logic into automaton functors.

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Ul Haq Bokhary, Syed Ahtsham, Muhammad Imran, Shehnaz Akhter, and Sadia Manzoor. "Molecular topological invariants of certain chemical networks." Main Group Metal Chemistry 44, no. 1 (January 1, 2021): 141–49. http://dx.doi.org/10.1515/mgmc-2021-0010.

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Abstract Topological descriptors are the graph invariants that are used to explore the molecular topology of the molecular/chemical graphs. In QSAR/QSPR research, physico-chemical characteristics and topological invariants including Randić, atom-bond connectivity, and geometric arithmetic invariants are utilized to corelate and estimate the structure relationship and bioactivity of certain chemical compounds. Graph theory and discrete mathematics have discovered an impressive utilization in the area of research. In this article, we investigate the valency-depended invariants for certain chemical networks like generalized Aztec diamonds and tetrahedral diamond lattice. Moreover, the exact values of invariants for these categories of chemical networks are derived.

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Ferri, Massimo. "Colour Switching and Homeomorphism of Manifolds." Canadian Journal of Mathematics 39, no. 1 (February 1, 1987): 8–32. http://dx.doi.org/10.4153/cjm-1987-002-5.

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Throughout this paper, we work in the PL and pseudosimplicial categories, for which we refer to [17] and [10] respectively. For the graph theory involved see [9].An h-coloured graph (Γ, γ) is a multigraph Γ = (V(Γ), E(Γ)) regular of degree h, endowed with an edge-coloration γ by h colours. If is the colour set, for each we setFor each set . For n ∊ Z, n ≧ 1, setΔn will be mostly used to denote the colour set for an (n + 1)-coloured graph.

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FOUNTOULAKIS, NIKOLAOS, and KONSTANTINOS PANAGIOTOU. "3-Connected Cores In Random Planar Graphs." Combinatorics, Probability and Computing 20, no. 3 (January 24, 2011): 381–412. http://dx.doi.org/10.1017/s0963548310000532.

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The study of the structural properties of large random planar graphs has become in recent years a field of intense research in computer science and discrete mathematics. Nowadays, a random planar graph is an important and challenging model for evaluating methods that are developed to study properties of random graphs from classes with structural side constraints.In this paper we focus on the structure of random 2-connected planar graphs regarding the sizes of their 3-connected building blocks, which we callcores. In fact, we prove a general theorem regarding random biconnected graphs from various classes. IfBnis a graph drawn uniformly at random from a suitable classof labelled biconnected graphs, then we show that with probability 1 −o(1) asn→ ∞,Bnbelongs to exactly one of the following categories:(i)either there is a uniquegiantcore inBn, that is, there is a 0 <c=c() < 1 such that the largest core contains ~cnvertices, and every other core contains at mostnαvertices, where 0 < α = α() < 1;(ii)or all cores ofBncontainO(logn) vertices.Moreover, we find the critical condition that determines the category to whichBnbelongs, and also provide sharp concentration results for the counts of cores of all sizes between 1 andn. As a corollary, we obtain that a random biconnected planar graph belongs to category (i), where in particularc= 0.765. . . and α = 2/3.

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Mordecai, Yaniv, James P. Fairbanks, and Edward F. Crawley. "Category-Theoretic Formulation of the Model-Based Systems Architecting Cognitive-Computational Cycle." Applied Sciences 11, no. 4 (February 23, 2021): 1945. http://dx.doi.org/10.3390/app11041945.

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We introduce the Concept→Model→Graph→View Cycle (CMGVC). The CMGVC facilitates coherent architecture analysis, reasoning, insight, and decision making based on conceptual models that are transformed into a generic, robust graph data structure (GDS). The GDS is then transformed into multiple views of the model, which inform stakeholders in various ways. This GDS-based approach decouples the view from the model and constitutes a powerful enhancement of model-based systems engineering (MBSE). The CMGVC applies the rigorous foundations of Category Theory, a mathematical framework of representations and transformations. We show that modeling languages are categories, drawing an analogy to programming languages. The CMGVC architecture is superior to direct transformations and language-coupled common representations. We demonstrate the CMGVC to transform a conceptual system architecture model built with the Object Process Modeling Language (OPM) into dual graphs and a stakeholder-informing matrix that stimulates system architecture insight.

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GARVER, ALEXANDER, and THOMAS MCCONVILLE. "ORIENTED FLIP GRAPHS, NONCROSSING TREE PARTITIONS, AND REPRESENTATION THEORY OF TILING ALGEBRAS." Glasgow Mathematical Journal 62, no. 1 (February 7, 2019): 147–82. http://dx.doi.org/10.1017/s0017089519000028.

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AbstractThe purpose of this paper is to understand lattices of certain subcategories in module categories of representation-finite gentle algebras called tiling algebras, as introduced by Coelho Simões and Parsons. We present combinatorial models for torsion pairs and wide subcategories in the module category of tiling algebras. Our models use the oriented flip graphs and noncrossing tree partitions, previously introduced by the authors, and a description of the extension spaces between indecomposable modules over tiling algebras. In addition, we classify two-term simple-minded collections in bounded derived categories of tiling algebras. As a consequence, we obtain a characterization of c-matrices for any quiver mutation-equivalent to a type A Dynkin quiver.

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Dissertations / Theses on the topic "Graph theory. Categories (Mathematics)"

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Plessas, Demitri Joel. "Topos-like properties in two categories of graphs and graph-like features in an abstract category." CONNECT TO THIS TITLE ONLINE, 2008. http://etd.lib.umt.edu/theses/available/etd-05292008-131250/.

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Kissinger, Aleks. "Pictures of processes : automated graph rewriting for monoidal categories and applications to quantum computing." Thesis, University of Oxford, 2011. http://ora.ox.ac.uk/objects/uuid:61fb3161-a353-48fc-8da2-6ce220cce6a2.

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This work is about diagrammatic languages, how they can be represented, and what they in turn can be used to represent. More specifically, it focuses on representations and applications of string diagrams. String diagrams are used to represent a collection of processes, depicted as "boxes" with multiple (typed) inputs and outputs, depicted as "wires". If we allow plugging input and output wires together, we can intuitively represent complex compositions of processes, formalised as morphisms in a monoidal category. While string diagrams are very intuitive, existing methods for defining them rigorously rely on topological notions that do not extend naturally to automated computation. The first major contribution of this dissertation is the introduction of a discretised version of a string diagram called a string graph. String graphs form a partial adhesive category, so they can be manipulated using double-pushout graph rewriting. Furthermore, we show how string graphs modulo a rewrite system can be used to construct free symmetric traced and compact closed categories on a monoidal signature. The second contribution is in the application of graphical languages to quantum information theory. We use a mixture of diagrammatic and algebraic techniques to prove a new classification result for strongly complementary observables. Namely, maximal sets of strongly complementary observables of dimension D must be of size no larger than 2, and are in 1-to-1 correspondence with the Abelian groups of order D. We also introduce a graphical language for multipartite entanglement and illustrate a simple graphical axiom that distinguishes the two maximally-entangled tripartite qubit states: GHZ and W. Notably, we illustrate how the algebraic structures induced by these operations correspond to the (partial) arithmetic operations of addition and multiplication on the complex projective line. The third contribution is a description of two software tools developed in part by the author to implement much of the theoretical content described here. The first tool is Quantomatic, a desktop application for building string graphs and graphical theories, as well as performing automated graph rewriting visually. The second is QuantoCoSy, which performs fully automated, model-driven theory creation using a procedure called conjecture synthesis.

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Grinshpun, Andrey Vadim. "Some problems in Graph Ramsey Theory." Thesis, Massachusetts Institute of Technology, 2015. http://hdl.handle.net/1721.1/97767.

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Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2015.
This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.
Cataloged from student-submitted PDF version of thesis.
Includes bibliographical references (pages 149-156).
A graph G is r-Ramsey minimal with respect to a graph H if every r-coloring of the edges of G yields a monochromatic copy of H, but the same is not true for any proper subgraph of G. The study of the properties of graphs that are Ramsey minimal with respect to some H and similar problems is known as graph Ramsey theory; we study several problems in this area. Burr, Erdös, and Lovász introduced s(H), the minimum over all G that are 2- Ramsey minimal for H of [delta](G), the minimum degree of G. We find the values of s(H) for several classes of graphs H, most notably for all 3-connected bipartite graphs which proves many cases of a conjecture due to Szabó, Zumstein, and Zürcher. One natural question when studying graph Ramsey theory is what happens when, rather than considering all 2-colorings of a graph G, we restrict to a subset of the possible 2-colorings. Erdös and Hajnal conjectured that, for any fixed color pattern C, there is some [epsilon] > 0 so that every 2-coloring of the edges of a Kn, the complete graph on n vertices, which doesn't contain a copy of C contains a monochromatic clique on n[epsilon] vertices. Hajnal generalized this conjecture to more than 2 colors and asked in particular about the case when the number of colors is 3 and C is a rainbow triangle (a K3 where each edge is a different color); we prove Hajnal's conjecture for rainbow triangles. One may also wonder what would happen if we wish to cover all of the vertices with monochromatic copies of graphs. Let F = {F₁, F₂, . . .} be a sequence of graphs such that Fn is a graph on n vertices with maximum degree at most [delta]. If each Fn is bipartite, then the vertices of any 2-edge-colored complete graph can be partitioned into at most 2C[delta] vertex disjoint monochromatic copies of graphs from F, where C is an absolute constant. This result is best possible, up to the constant C.
by Andrey Vadim Grinshpun.
Ph. D.

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Al, Shumrani Mohammed Ahmed Musa. "Homotopy theory in algebraic derived categories." Thesis, University of Glasgow, 2006. http://theses.gla.ac.uk/1905/.

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In this thesis, we introduce some new notions in the derived category D+(fg) (R) of bounded below chain complexes of finite type over local commutative noetherian ring R with maximal ideal m and residue field K in chapter three and study their relations to each other. Also, we set up the Adams spectral sequence for chain complexes in D+(f,g) (R) in chapter four and study its convergence. To accomplish this task, we give two background chapters. We give some good account of chain complexes in chapter one. We review some basic homological algebra and give definition and basic properties of chain complexes. Then we study the homotopy category of chain complexes and we end chapter one with section about spectral sequences. Chapter two is about the derived category of a commutative ring. Section one is about localization of categories and left and right fractions. Then in section two, we give definition of triangulated categories and some of its basic properties and we end section two with definitions of homotopy limits and colimits. In section three, we show that the derived category is a triangulated category. In section four, we give definitions of the derived functors, the derived tensor product and the derived Hom. In chapter three, we start section one by giving some facts about local rings and we end this section by showing that every bounded below chain complex of finite type has a minimal free resolution. In section two, we show a derived analog of the Whitehead Theorem. In section three, we construct Postnikov towers for chain complexes. In section four, we define the Steenrod algebra. In section five, six and seven, we define irreducible, atomic, minimal atomic, no mod m detectable homology, H*-monogenic, nuclear chain complexes and the core of a chain complex. We show some various results relating these notions to each other and give some examples. In chapter four, we set up the Adams spectral sequence in section one and study its properties. In section two, we study homology localization and local homology. In section three, we define K[0]-nilpotent completion and we show that the Adams spectral sequence for a chain complex Y converges strongly to the homology of the K[0]-nilpotent completion of Y. In section four, we study the Adams spectral sequence’s convergence where we show that the K[0]-nilpotent completion for a bounded chain complex Y consisting of finitely generated free R-modules in each degree is isomorphic to the localization of Y with respect to the H*(—, K)-theory. In section five, we present some examples.

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Garbe, Frederik. "Extremal graph theory via structural analysis." Thesis, University of Birmingham, 2018. http://etheses.bham.ac.uk//id/eprint/8869/.

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We discuss two extremal problems in extremal graph theory. First we establish a precise characterisation of 4-uniform hypergraphs with minimum codegree close to n/2 which contain a Hamilton 2-cycle. As a corollary we determine the exact Dirac threshold for Hamilton 2-cycles in 4-uniform hypergraphs, and we provide a polynomial-time algorithm which answers the corresponding decision problem for 4-graphs with minimum degree close to n/2. In contrast we also show that the corresponding decision problem for tight Hamilton cycles in dense k-graphs is NP-complete. Furthermore we study the following bootstrap percolation process: given a connected graph G, we infect an initial set A of vertices, and in each step a vertex v becomes infected if at least a p-proportion of its neighbours are infected. A set A which infects the whole graph is called a contagious set. Our main result states that for every pin (0,1] and for every connected graph G on n vertices the minimal size of a contagious set is less than 2pn or 1. This result is best-possible, but we provide a stronger bound in the case of graphs of girth at least five. Both proofs exploit the structure of a minimal counterexample.

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Fiala, Nick C. "Some topics in combinatorial design theory and algebraic graph theory /." The Ohio State University, 2002. http://rave.ohiolink.edu/etdc/view?acc_num=osu1486402957198077.

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Poklewski-Koziell, Rowan. "Extensive categories, commutative semirings and Galois theory." Master's thesis, Faculty of Science, 2020. http://hdl.handle.net/11427/32412.

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We describe the Galois theory of commutative semirings as a Boolean Galois theory in the sense of Carboni and Janelidze. Such a Galois structure then naturally suggests an extension to commutative semirings of the classical theory of quadratic equations over commutative rings. We show, however, that our proposed generalization is impossible for connected commutative semirings which are not rings, leading to the conclusion that for the theory of quadratic equations, “minus is needed”. Finally, by considering semirings B which have no non-trivial additive inverses and no non-trivial zero divisors, we present an example of a normal extension of commutative semirings which has an underlying B-semimodule structure isomorphic to B×B.

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Edwards, C. S. "Some extremal problems in graph theory." Thesis, University of Reading, 1986. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.373467.

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Weaver, Robert Wooddell. "Some problems in structural graph theory /." The Ohio State University, 1986. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487268021746449.

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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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Books on the topic "Graph theory. Categories (Mathematics)"

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Hasegawa, Masahito. Models of sharing graphs: A categorical semantics of let and letrec. New York: Springer, 1999.

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1942-, Knauer U., and Mikhalev A. V, eds. Monoids, acts, and categories: With applications to wreath products and graphs : a handbook for students and researchers. Berlin: W. de Gruyter, 2000.

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

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Awodey, Steve. Category theory. New York: Oxford University Press Inc., 2006.

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Higher topos theory. Princeton, N.J: Princeton University Press, 2009.

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Homotopy theory of higher categories. Cambridge: Cambridge University Press, 2012.

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Simpson, Carlos. Homotopy Theory of Higher Categories: From Segal Categories to n-Categories and Beyond. Cambridge: Cambridge University Press, 2011.

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Chemical graph theory. 2nd ed. Boca Raton: CRC Press, 1992.

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M, Parmenter Michael, ed. Discrete mathematics with graph theory. 3rd ed. Upper Saddle River, N.J: Pearson Prentice Hall, 2006.

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M, Parmenter Michael, ed. Discrete mathematics with graph theory. Upper Saddle River, NJ: Prentice Hall, 1998.

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Book chapters on the topic "Graph theory. Categories (Mathematics)"

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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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Fortney, Jon Pierre. "Graph Theory." In Discrete Mathematics for Computer Science, 167–94. First edition. | Boca Raton : C&H/CRC Press, 2021.: Chapman and Hall/CRC, 2020. http://dx.doi.org/10.1201/9781003091479-9.

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Nievergelt, Yves. "Graph Theory." In Foundations of Logic and Mathematics, 361–98. Boston, MA: Birkhäuser Boston, 2002. http://dx.doi.org/10.1007/978-1-4612-0125-0_8.

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Wallis, W. D. "Graph Theory." In A Beginner's Guide to Finite Mathematics, 157–209. Boston: Birkhäuser Boston, 2012. http://dx.doi.org/10.1007/978-0-8176-8319-1_4.

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Wallis, W. D. "Graph Theory." In A Beginner's Guide to Discrete Mathematics, 215–62. Boston: Birkhäuser Boston, 2012. http://dx.doi.org/10.1007/978-0-8176-8286-6_7.

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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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Bagdasar, Ovidiu. "Elements of Graph Theory." In Concise Computer Mathematics, 73–80. Cham: Springer International Publishing, 2013. http://dx.doi.org/10.1007/978-3-319-01751-8_9.

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Turaev, Vladimir, and Alexis Virelizier. "The state sum graph TQFT." In Monoidal Categories and Topological Field Theory, 321–98. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-49834-8_15.

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Aluffi, Paolo. "Preliminaries: Set theory and categories." In Graduate Studies in Mathematics, 1–39. Providence, Rhode Island: American Mathematical Society, 2009. http://dx.doi.org/10.1090/gsm/104/01.

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Conference papers on the topic "Graph theory. Categories (Mathematics)"

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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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Kusmayadi, Tri Atmojo, and Nugroho Arif Sudibyo. "The eccentric digraph of caterpillar graph and generalized Jahangir graph." In THE THIRD INTERNATIONAL CONFERENCE ON MATHEMATICS: Education, Theory and Application. AIP Publishing, 2021. http://dx.doi.org/10.1063/5.0040222.

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Pratama, Javas Alfreda Belva Yoga, and Tri Atmojo Kusmayadi. "On the local metric dimension of dipyramidal graph and king graph." In THE THIRD INTERNATIONAL CONFERENCE ON MATHEMATICS: Education, Theory and Application. AIP Publishing, 2021. http://dx.doi.org/10.1063/5.0039319.

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Setiawan, Ekky Kurnia, and I. Ketut Budayasa. "Application of graph theory concept for traffic light control at crossroad." In INTERNATIONAL CONFERENCE ON MATHEMATICS: PURE, APPLIED AND COMPUTATION: Empowering Engineering using Mathematics. Author(s), 2017. http://dx.doi.org/10.1063/1.4994457.

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Khasanah, Himawanti Rizqi, Putranto Hadi Utomo, and Bowo Winarno. "Schemes of network coding on fan graph F2,4 and closed helm graph CH4." In THE THIRD INTERNATIONAL CONFERENCE ON MATHEMATICS: Education, Theory and Application. AIP Publishing, 2021. http://dx.doi.org/10.1063/5.0039774.

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Rahmawati, Ami, Vika Yugi Kurniawan, and Supriyadi Wibowo. "The diameter of annihilator ideal graph of ℤn." In THE THIRD INTERNATIONAL CONFERENCE ON MATHEMATICS: Education, Theory and Application. AIP Publishing, 2021. http://dx.doi.org/10.1063/5.0039847.

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Akerina, A., and K. A. Sugeng. "Graceful labeling on a multiple-fan graph with pendants." In THE THIRD INTERNATIONAL CONFERENCE ON MATHEMATICS: Education, Theory and Application. AIP Publishing, 2021. http://dx.doi.org/10.1063/5.0039411.

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Ashidiqi, Muhammad Rofi’, Vika Yugi Kurniawan, and Putranto Hadi Utomo. "The diameter of annihilator graph of non-commutative semirings." In THE THIRD INTERNATIONAL CONFERENCE ON MATHEMATICS: Education, Theory and Application. AIP Publishing, 2021. http://dx.doi.org/10.1063/5.0042278.

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Voytsekhovich, Vyacheslav Emerikovich. "Mathematics of the future." In 4th International Conference “Futurity designing. Digital reality problems”. Keldysh Institute of Applied Mathematics, 2021. http://dx.doi.org/10.20948/future-2021-8.

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Abstract:

Mathematics has entered a crisis of complexity. The main reason is the use of immutable concepts according to the law of identity of Aristotle's logic. The evidence has become super-long, unverifiable. Overcoming the crisis is possible in the transition from immutable concepts to "mobile" ones, in the generalization of the law of identity. In modern mathematics, there are prerequisites for such a transition – in qualitative theory, probability theory, algorithm theory, and foundations. The future of mathematics lies in the development of categories as transformative concepts.

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Mariiaa, Haniiam, Vika Yugi Kurniawan, and Sutrima. "Zero annihilator graph of semiring of matrices over Boolean semiring." In THE THIRD INTERNATIONAL CONFERENCE ON MATHEMATICS: Education, Theory and Application. AIP Publishing, 2021. http://dx.doi.org/10.1063/5.0039557.

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Reports on the topic "Graph theory. Categories (Mathematics)"

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Robertson, Neil, and Paul Seymour. Graph Structure Theory: Proceedings of a Joint Summer Research Conference on Graph Minors Held June 22 to July 5, 1991, at the University of Washington, Seattle. Contemporary Mathematics 147. Fort Belvoir, VA: Defense Technical Information Center, January 1991. http://dx.doi.org/10.21236/ada266435.

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