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Chromatic Polynomials and Chromaticity of Graphs

Author: F. M. Dong

Publisher: World Scientific

Published: 2005

Total Pages: 388

ISBN-13: 9812563172

"This is the first book to comprehensively cover chromatic polynomials of graphs. It includes most of the known results and unsolved problems in the area of chromatic polynomials. Dividing the book into three main parts, the authors take readers from the rudiments of chromatic polynomials to more complex topics: the chromatic equivalence classes of graphs and the zeros and inequalities of chromatic polynomials. The early material is well suited to a graduate level course while the latter parts will be an invaluable resource for postgraduate students and researchers in combinatorics and graph theory."--BOOK JACKET.

Graph Polynomials

Author: Yongtang Shi

Publisher: CRC Press

Published: 2016-11-25

Total Pages: 174

ISBN-13: 1315350963

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This book covers both theoretical and practical results for graph polynomials. Graph polynomials have been developed for measuring combinatorial graph invariants and for characterizing graphs. Various problems in pure and applied graph theory or discrete mathematics can be treated and solved efficiently by using graph polynomials. Graph polynomials have been proven useful areas such as discrete mathematics, engineering, information sciences, mathematical chemistry and related disciplines.

A Walk Through Combinatorics

Author: Mikl¢s B¢na

Publisher: World Scientific

Published: 2006

Total Pages: 492

ISBN-13: 9812568859

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This is a textbook for an introductory combinatorics course that can take up one or two semesters. An extensive list of problems, ranging from routine exercises to research questions, is included. In each section, there are also exercises that contain material not explicitly discussed in the preceding text, so as to provide instructors with extra choices if they want to shift the emphasis of their course. Just as with the first edition, the new edition walks the reader through the classic parts of combinatorial enumeration and graph theory, while also discussing some recent progress in the area: on the one hand, providing material that will help students learn the basic techniques, and on the other hand, showing that some questions at the forefront of research are comprehensible and accessible for the talented and hard-working undergraduate. The basic topics discussed are: the twelvefold way, cycles in permutations, the formula of inclusion and exclusion, the notion of graphs and trees, matchings and Eulerian and Hamiltonian cycles. The selected advanced topics are: Ramsey theory, pattern avoidance, the probabilistic method, partially ordered sets, and algorithms and complexity. As the goal of the book is to encourage students to learn more combinatorics, every effort has been made to provide them with a not only useful, but also enjoyable and engaging reading.

Chromaticity of Hypergraphs

Author: Syed Ahtsham Ul Haq Bokhary

Publisher: LAP Lambert Academic Publishing

Published: 2011-10

Total Pages: 80

ISBN-13: 9783846533888

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The coloring the vertices of a graph is one of the fundamental concepts of graph theory. It is widely believed that coloring was first mentioned in 1852 when Francis Guthrie asked if four colors are enough to color any geographic map in such a way that no two countries sharing a common border would have the same color. If we denote the countries by points in the plane and connect each pair of points that correspond to two countries with a common border by a curve, we obtain a planar graph. The celebrated four color problem asks if every planer graph can be colored with 4 colors. The four color problem became one of the most famous problem in discrete mathematics of the 20th century. This has spawned the development of many useful tools for solving graph coloring problems. The coloring of hypergraphs started in 1966 when P. Erdos and A. Hajnal introduced the notion of coloring of a hypergraph and obtained the first important results. Since then many results in graph colorings have been extended to hyper- graphs. This work focuses on the chromatic polynomial and chromatic uniqueness of hypergraphs.

Operator Calculus On Graphs: Theory And Applications In Computer Science

Author: George Stacey Staples

Publisher: World Scientific

Published: 2012-02-23

Total Pages: 428

ISBN-13: 1908977574

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This pioneering book presents a study of the interrelationships among operator calculus, graph theory, and quantum probability in a unified manner, with significant emphasis on symbolic computations and an eye toward applications in computer science.Presented in this book are new methods, built on the algebraic framework of Clifford algebras, for tackling important real world problems related, but not limited to, wireless communications, neural networks, electrical circuits, transportation, and the world wide web. Examples are put forward in Mathematica throughout the book, together with packages for performing symbolic computations.

New Trends in Algebras and Combinatorics

Author: K. P. Shum

Publisher:

Published: 2020

Total Pages: 498

ISBN-13: 9811215472

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Chromatic Polynomials for Graphs with Split Vertices

Author: Sarah E. Adams

Publisher:

Published: 2020

Total Pages: 49

ISBN-13:

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Graph theory is a branch of mathematics that uses graphs as a mathematical structure to model relations between objects. Graphs can be categorized in a wide variety of graph families. One important instrument to classify graphs is the chromatic polynomial. This was introduced by Birkhoff in 1912 and allowed to further study and develop several graph related problems. In this thesis, we study some problems that can be approached using the chromatic polynomial. In the first chapter, we introduce general definitions and examples of graphs. In the second chapter, we talk about graph colorings, the greedy algorithm, and give a short description for the four color problem. In the third chapter, we introduce the chromatic polynomial, study its property, and give some examples of computations. All of these are classical results. In chapter 4, we introduce colorings of graphs with split vertices, and give an application to the scheduling problem. Also, we show how the chromatic polynomial can be used in that setting. This is our "semi-original" contribution. Finally, in the last chapter, we talk about distance two colorings for graphs, and give examples on how this applies to coloring maps.

Harmony of Grbner Bases and the Modern Industrial Society

Author: Takayuki Hibi

Publisher: World Scientific

Published: 2012

Total Pages: 385

ISBN-13: 9814383465

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This volume consists of research papers and expository survey articles presented by the invited speakers of the conference on OC Harmony of GrAbner Bases and the Modern Industrial SocietyOCO. Topics include computational commutative algebra, algebraic statistics, algorithms of D-modules and combinatorics. This volume also provides current trends on GrAbner bases and will stimulate further development of many research areas surrounding GrAbner bases."

Groups, Combinatorics and Geometry

Author: Martin W. Liebeck

Publisher: Cambridge University Press

Published: 1992-09-10

Total Pages: 505

ISBN-13: 0521406854

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This volume contains a collection of papers on the subject of the classification of finite simple groups.

Erwin Schrödinger's Color Theory

Author: Keith K. Niall

Publisher: Springer

Published: 2017-12-05

Total Pages: 193

ISBN-13: 3319646214

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This book presents the most complete translation to date of Erwin Schrödinger’s work on colorimetry. In his work Schrödinger proposed a projective geometry of color space, rather than a Euclidean line-element. He also proposed new (at the time) colorimetric methods – in detail and at length - which represented a dramatic conceptual shift in colorimetry. Schrödinger shows how the trichromatic (or Young-Helmholtz) theory of color and the opponent-process (or Hering) theory of color are formally the same theory, or at least only trivially different. These translations of Schrödinger’s bold concepts for color space have a fresh resonance and importance for contemporary color theory.