Discrete Mathematics and Symmetry

Discrete Mathematics and Symmetry
Title Discrete Mathematics and Symmetry PDF eBook
Author Angel Garrido
Publisher MDPI
Pages 458
Release 2020-03-05
Genre Mathematics
ISBN 3039281909

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Some of the most beautiful studies in Mathematics are related to Symmetry and Geometry. For this reason, we select here some contributions about such aspects and Discrete Geometry. As we know, Symmetry in a system means invariance of its elements under conditions of transformations. When we consider network structures, symmetry means invariance of adjacency of nodes under the permutations of node set. The graph isomorphism is an equivalence relation on the set of graphs. Therefore, it partitions the class of all graphs into equivalence classes. The underlying idea of isomorphism is that some objects have the same structure if we omit the individual character of their components. A set of graphs isomorphic to each other is denominated as an isomorphism class of graphs. The automorphism of a graph will be an isomorphism from G onto itself. The family of all automorphisms of a graph G is a permutation group.

Symmetry in Graphs

Symmetry in Graphs
Title Symmetry in Graphs PDF eBook
Author Ted Dobson
Publisher Cambridge University Press
Pages 527
Release 2022-05-12
Genre Language Arts & Disciplines
ISBN 1108429068

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The first full-length book on the theme of symmetry in graphs, a fast-growing topic in algebraic graph theory.

A Spiral Workbook for Discrete Mathematics

A Spiral Workbook for Discrete Mathematics
Title A Spiral Workbook for Discrete Mathematics PDF eBook
Author Harris Kwong
Publisher Open SUNY Textbooks
Pages 298
Release 2015-11-06
Genre Mathematics
ISBN 9781942341161

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A Spiral Workbook for Discrete Mathematics covers the standard topics in a sophomore-level course in discrete mathematics: logic, sets, proof techniques, basic number theory, functions,relations, and elementary combinatorics, with an emphasis on motivation. The text explains and claries the unwritten conventions in mathematics, and guides the students through a detailed discussion on how a proof is revised from its draft to a nal polished form. Hands-on exercises help students understand a concept soon after learning it. The text adopts a spiral approach: many topics are revisited multiple times, sometimes from a dierent perspective or at a higher level of complexity, in order to slowly develop the student's problem-solving and writing skills.

Symmetry in Graph Theory

Symmetry in Graph Theory
Title Symmetry in Graph Theory PDF eBook
Author Jose M. Rodriguez
Publisher MDPI
Pages 340
Release 2019-03-14
Genre Mathematics
ISBN 303897658X

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This book contains the successful invited submissions to a Special Issue of Symmetry on the subject of “Graph Theory”. Although symmetry has always played an important role in Graph Theory, in recent years, this role has increased significantly in several branches of this field, including but not limited to Gromov hyperbolic graphs, the metric dimension of graphs, domination theory, and topological indices. This Special Issue includes contributions addressing new results on these topics, both from a theoretical and an applied point of view.

Discrete Geometry and Symmetry

Discrete Geometry and Symmetry
Title Discrete Geometry and Symmetry PDF eBook
Author Marston D. E. Conder
Publisher Springer
Pages 349
Release 2018-06-11
Genre Mathematics
ISBN 331978434X

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This book consists of contributions from experts, presenting a fruitful interplay between different approaches to discrete geometry. Most of the chapters were collected at the conference “Geometry and Symmetry” in Veszprém, Hungary from 29 June to 3 July 2015. The conference was dedicated to Károly Bezdek and Egon Schulte on the occasion of their 60th birthdays, acknowledging their highly regarded contributions in these fields. While the classical problems of discrete geometry have a strong connection to geometric analysis, coding theory, symmetry groups, and number theory, their connection to combinatorics and optimization has become of particular importance. The last decades have seen a revival of interest in discrete geometric structures and their symmetry. The rapid development of abstract polytope theory has resulted in a rich theory featuring an attractive interplay of methods and tools from discrete geometry, group theory and geometry, combinatorial group theory, and hyperbolic geometry and topology. This book contains papers on new developments in these areas, including convex and abstract polytopes and their recent generalizations, tiling and packing, zonotopes, isoperimetric inequalities, and on the geometric and combinatorial aspects of linear optimization. The book is a valuable resource for researchers, both junior and senior, in the field of discrete geometry, combinatorics, or discrete optimization. Graduate students find state-of-the-art surveys and an open problem collection.

Symmetric Designs

Symmetric Designs
Title Symmetric Designs PDF eBook
Author Eric S. Lander
Publisher Cambridge University Press
Pages 321
Release 1983-01-20
Genre Mathematics
ISBN 052128693X

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Symmetric designs are an important class of combinatorial structures which arose first in the statistics and are now especially important in the study of finite geometries. This book presents some of the algebraic techniques that have been brought to bear on the question of existence, construction and symmetry of symmetric designs - including methods inspired by the algebraic theory of coding and by the representation theory of finite groups - and includes many results. Rich in examples and containing over 100 problems, the text also provides an introduction to many of the modern algebraic approaches used, through six lengthy appendices and supplementary problems. The book will be of interest to both combinatorialists and algebraists, and could be used as a course text for a graduate course.

Frameworks, Tensegrities, and Symmetry

Frameworks, Tensegrities, and Symmetry
Title Frameworks, Tensegrities, and Symmetry PDF eBook
Author Robert Connelly
Publisher Cambridge University Press
Pages 299
Release 2022-01-27
Genre Mathematics
ISBN 0521879108

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Why don't things fall down? Engineering meets mathematics in this introduction to the geometry of rigid and flexible structures.