Discrete Mathematics And Symmetry PDF Download
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Author | : Angel Garrido |
Publisher | : MDPI |
Total Pages | : 458 |
Release | : 2020-03-05 |
Genre | : Mathematics |
ISBN | : 3039281909 |
Download Discrete Mathematics and Symmetry Book in PDF, ePub and Kindle
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.
Author | : Angel Garrido |
Publisher | : |
Total Pages | : 458 |
Release | : 2020 |
Genre | : Mathematics |
ISBN | : 9783039281916 |
Download Discrete Mathematics and Symmetry Book in PDF, ePub and Kindle
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.
Author | : Isla Harvey |
Publisher | : Murphy & Moore Publishing |
Total Pages | : 0 |
Release | : 2023-09-19 |
Genre | : Mathematics |
ISBN | : 9781639877461 |
Download Applications of Symmetry in Discrete Mathematics Book in PDF, ePub and Kindle
Discrete mathematics refers to the study of mathematical structures that are countable or otherwise separable or unique. Logical statements, combinations and graphs are examples of discrete structures. Symmetry is a proportionate and balanced resemblance between two halves of an object. It implies that one half is the mirror image of the other. Discrete symmetry in mathematics is a symmetry that explains non-continuous changes in a system. Symmetry is frequently used in discrete mathematics to show relationships between two or more elements of a set, where the first element relates to the second element and vice-versa. This book explores all the important aspects of discrete mathematics and symmetry in the present day scenario. It presents researches and studies performed by experts across the globe. This book, with its detailed analyses and data, will prove immensely beneficial to professionals and students involved in this area of mathematics at various levels.
Author | : Karl Heinrich Hofmann |
Publisher | : |
Total Pages | : 188 |
Release | : 1991 |
Genre | : Discrete groups |
ISBN | : |
Download Symmetry of Discrete Mathematical Structures and Their Symmetry Groups Book in PDF, ePub and Kindle
Author | : Marston D. E. Conder |
Publisher | : Springer |
Total Pages | : 333 |
Release | : 2018-06-11 |
Genre | : Mathematics |
ISBN | : 331978434X |
Download Discrete Geometry and Symmetry Book in PDF, ePub and Kindle
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.
Author | : Robert Connelly |
Publisher | : Springer |
Total Pages | : 378 |
Release | : 2014-06-11 |
Genre | : Mathematics |
ISBN | : 1493907816 |
Download Rigidity and Symmetry Book in PDF, ePub and Kindle
This book contains recent contributions to the fields of rigidity and symmetry with two primary focuses: to present the mathematically rigorous treatment of rigidity of structures and to explore the interaction of geometry, algebra and combinatorics. Contributions present recent trends and advances in discrete geometry, particularly in the theory of polytopes. 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, classical geometry, hyperbolic geometry and topology. Overall, the book shows how researchers from diverse backgrounds explore connections among the various discrete structures with symmetry as the unifying theme. The volume will be a valuable source as an introduction to the ideas of both combinatorial and geometric rigidity theory and its applications, incorporating the surprising impact of symmetry. It will appeal to students at both the advanced undergraduate and graduate levels, as well as post docs, structural engineers and chemists.
Author | : Ted Dobson |
Publisher | : Cambridge University Press |
Total Pages | : 527 |
Release | : 2022-05-12 |
Genre | : Language Arts & Disciplines |
ISBN | : 1108429068 |
Download Symmetry in Graphs Book in PDF, ePub and Kindle
The first full-length book on the theme of symmetry in graphs, a fast-growing topic in algebraic graph theory.
Author | : Gena Hahn |
Publisher | : Springer Science & Business Media |
Total Pages | : 434 |
Release | : 2013-03-14 |
Genre | : Mathematics |
ISBN | : 9401589372 |
Download Graph Symmetry Book in PDF, ePub and Kindle
The last decade has seen two parallel developments, one in computer science, the other in mathematics, both dealing with the same kind of combinatorial structures: networks with strong symmetry properties or, in graph-theoretical language, vertex-transitive graphs, in particular their prototypical examples, Cayley graphs. In the design of large interconnection networks it was realised that many of the most fre quently used models for such networks are Cayley graphs of various well-known groups. This has spawned a considerable amount of activity in the study of the combinatorial properties of such graphs. A number of symposia and congresses (such as the bi-annual IWIN, starting in 1991) bear witness to the interest of the computer science community in this subject. On the mathematical side, and independently of any interest in applications, progress in group theory has made it possible to make a realistic attempt at a complete description of vertex-transitive graphs. The classification of the finite simple groups has played an important role in this respect.
Author | : Jose M. Rodriguez |
Publisher | : MDPI |
Total Pages | : 340 |
Release | : 2019-03-14 |
Genre | : Mathematics |
ISBN | : 303897658X |
Download Symmetry in Graph Theory Book in PDF, ePub and Kindle
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.
Author | : Isla Harvey |
Publisher | : States Academic Press |
Total Pages | : 0 |
Release | : 2023-09-19 |
Genre | : Mathematics |
ISBN | : 9781639897438 |
Download Discrete Geometry and Symmetry Book in PDF, ePub and Kindle
Discrete geometry refers to a subfield of geometry that examines discrete and highly symmetric structures in geometry and how discrete geometric objects might be constructed. It is closely connected to computational geometry as well as other mathematical subjects including combinatorial geometry and topology, combinatorial optimization, geometric graph theory, and finite geometry. Discrete geometry focuses on the problems that aim to characterize specific discrete arrangements of geometric objects having high symmetry. Many of the techniques used to investigate discrete arrangements are based on a wide range of symetrizations. Discrete geometry is used in numerous theoretical disciplines including algebraic geometry and topology, geometry of numbers, mathematical physics, functional analysis, geometric measure theory, calculus of variations, and group theory. This book is compiled in such a manner, that it will provide an in-depth knowledge about the theory and applications of discrete geometry and symmetry. It is a resource guide for experts as well as students.