Download or read book Bipartite Distance regular Graphs and Their Primitive Idempotents written by Mark Spruill MacLean and published by . This book was released on 2001 with total page 106 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Bipartite Distance regular Graphs written by Brian Curtin and published by . This book was released on 1996 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Distance Regular Graphs written by Andries E. Brouwer and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 513 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ever since the discovery of the five platonic solids in ancient times, the study of symmetry and regularity has been one of the most fascinating aspects of mathematics. Quite often the arithmetical regularity properties of an object imply its uniqueness and the existence of many symmetries. This interplay between regularity and symmetry properties of graphs is the theme of this book. Starting from very elementary regularity properties, the concept of a distance-regular graph arises naturally as a common setting for regular graphs which are extremal in one sense or another. Several other important regular combinatorial structures are then shown to be equivalent to special families of distance-regular graphs. Other subjects of more general interest, such as regularity and extremal properties in graphs, association schemes, representations of graphs in euclidean space, groups and geometries of Lie type, groups acting on graphs, and codes are covered independently. Many new results and proofs and more than 750 references increase the encyclopaedic value of this book.
Download or read book Some Problems in the Theory of Distance regular Graphs written by Benjamin V. C. Collins and published by . This book was released on 1996 with total page 206 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Some Results on Bipartite Distance regular Graphs written by Michael S. Lang and published by . This book was released on 2001 with total page 94 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Bipartite Distance Regular Graphs of Diameter Four written by Junbo Huang and published by . This book was released on 2014 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Using a method by Godsil and Roy, bipartite distance-regular graphs of diameter four can be used to construct $\{0,\alpha\}$-sets, a generalization of the widely applied equiangular sets and mutually unbiased bases. In this thesis, we study the properties of these graphs. There are three main themes of the thesis. The first is the connection between bipartite distance-regular graphs of diameter four and their halved graphs, which are necessarily strongly regular. We derive formulae relating the parameters of a graph of diameter four to those of its halved graphs, and use these formulae to derive a necessary condition for the point graph of a partial geometry to be a halved graph. Using this necessary condition, we prove that several important families of strongly regular graphs cannot be halved graphs. The second theme is the algebraic properties of the graphs. We study Krein parameters as the first part of this theme. We show that bipartite-distance regular graphs of diameter four have one "special" Krein parameter, denoted by $\krein$. We show that the antipodal bipartite distance-regular graphs of diameter four with $\krein=0$ are precisely the Hadamard graphs. In general, we show that a bipartite distance-regular graph of diameter four satisfies $\krein=0$ if and only if it satisfies the so-called $Q$-polynomial property. In relation to halved graphs, we derive simple formulae for computing the Krein parameters of a halved graph in terms of those of the bipartite graph. As the second part of the algebraic theme, we study Terwilliger algebras. We describe all the irreducible modules of the complex space under the Terwilliger algebra of a bipartite distance-regular graph of diameter four, and prove that no irreducible module can contain two linearly independent eigenvectors of the graph with the same eigenvalue. Finally, we study constructions and bounds of $\{0,\alpha\}$-sets as the third theme. We present some distance-regular graphs that provide new constructions of $\{0,\alpha\}$-sets. We prove bounds for the sizes of $\{0,\alpha\}$-sets of flat vectors, and characterize all the distance-regular graphs that yield $\{0,\alpha\}$-sets meeting the bounds at equality. We also study bipartite covers of linear Cayley graphs, and present a geometric condition and a coding theoretic condition for such a cover to produce $\{0,\alpha\}$-sets. Using simple operations on graphs, we show how new $\{0,\alpha\}$-sets can be constructed from old ones.
Download or read book Algebraic Combinatorics and the Monster Group written by Alexander A. Ivanov and published by Cambridge University Press. This book was released on 2023-08-17 with total page 584 pages. Available in PDF, EPUB and Kindle. Book excerpt: Covering, arguably, one of the most attractive and mysterious mathematical objects, the Monster group, this text strives to provide an insightful introduction and the discusses the current state of the field. The Monster group is related to many areas of mathematics, as well as physics, from number theory to string theory. This book cuts through the complex nature of the field, highlighting some of the mysteries and intricate relationships involved. Containing many meaningful examples and a manual introduction to the computer package GAP, it provides the opportunity and resources for readers to start their own calculations. Some 20 experts here share their expertise spanning this exciting field, and the resulting volume is ideal for researchers and graduate students working in Combinatorial Algebra, Group theory and related areas.
Download or read book Imprimitive Distance transitive Graphs written by Monther Rashed Furaidan and published by . This book was released on 2004 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book On the Terwilliger Algebra of Bipartite Distance regular Graphs written by Safet Penjić and published by . This book was released on 2019 with total page 107 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book D bounded Distance regular Graphs written by Chih-wen Weng and published by . This book was released on 1995 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Bipartite Graphs and their Applications written by Armen S. Asratian and published by Cambridge University Press. This book was released on 1998-08-13 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bipartite graphs are perhaps the most basic of objects in graph theory, both from a theoretical and practical point of view. However, sometimes they have been considered only as a special class in some wider context. This book deals solely with bipartite graphs. Together with traditional material, the reader will also find many unusual results. Essentially all proofs are given in full; many of these have been streamlined specifically for this text. Numerous exercises of all standards have also been included. The theory is illustrated with many applications especially to problems in timetabling, chemistry, communication networks and computer science. For the most part the material is accessible to any reader with a graduate understanding of mathematics. However, the book contains advanced sections requiring much more specialized knowledge, which will be of interest to specialists in combinatorics and graph theory.
Download or read book Q polynomial Structures for Association Schemes and Distance regular Graphs written by Garth A. Dickie and published by . This book was released on 1995 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Bipartite P and Q polynomial Association Schemes written by John Simon Caughman and published by . This book was released on 1998 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Journal of Algebraic Combinatorics written by and published by . This book was released on 2000 with total page 608 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book On Bipartite Q polynomial Distance Regular Graphs with C 2 written by Štefko Miklavič and published by . This book was released on 2004 with total page 16 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Distance In Graphs written by Fred Buckley and published by Addison Wesley Publishing Company. This book was released on 1990-01-21 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Abstracts of Papers Presented to the American Mathematical Society written by American Mathematical Society and published by . This book was released on 2003 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt:
