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El. knyga: Strongly Regular Graphs

(Universiteit Gent, Belgium), (Technische Universiteit Eindhoven, The Netherlands)
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Strongly regular graphs lie at the intersection of statistical design, group theory, finite geometry, information and coding theory, and extremal combinatorics. This monograph collects all the major known results together for the first time in book form, creating an invaluable text that researchers in algebraic combinatorics and related areas will refer to for years to come. The book covers the theory of strongly regular graphs, polar graphs, rank 3 graphs associated to buildings and Fischer groups, cyclotomic graphs, two-weight codes and graphs related to combinatorial configurations such as Latin squares, quasi-symmetric designs and spherical designs. It gives the complete classification of rank 3 graphs, including some new constructions. More than 100 graphs are treated individually. Some unified and streamlined proofs are featured, along with original material including a new approach to the (affine) half spin graphs of rank 5 hyperbolic polar spaces.

Strongly regular graphs are found in statistical design, finite group theory, coding theory and quantum information theory. This detailed survey of the theory and examples gathers the major results for the first time. It is an invaluable reference for researchers in graph theory, algebraic combinatorics, information theory and group theory.

Recenzijos

'This is a book the mathematics world has long been waiting for [ The book] is by two of the leading researchers in the field. An interested reader will find almost everything on strongly regular graphs.' Ulrich Tamm, MathSciNet

Daugiau informacijos

This monograph on strongly regular graphs is an invaluable reference for anybody working in algebraic combinatorics.
1. Graphs;
2. Polar spaces;
3. Graphs related to polar spaces;
4. Buildings;
5. Fischer spaces;
6. Golay codes, Witt designs, and Leech lattice;
7. Cyclotomic constructions;
8. Combinatorial constructions;
9. p-Ranks;
10. Individual graph descriptions;
11. Classification of rank 3 graphs;
12. Parameter table; References; Parameter Index; Author Index; Subject Index.
Andries E. Brouwer is Emeritus Professor at TU Eindhoven. He is the co-author of Distance Regular Graphs (1989), and the textbook Spectra of Graphs (2012). He received an honorary doctorate from Aalborg University, Denmark in 2004. H. Van Maldeghem is Senior Full Professor in the Department of Mathematics at Ghent University, Belgium. He is the author of Generalized Polygons (1998), co-author of Translation Generalized Quadrangles (2007) and co-editor of the Collected Works of Jacques Tits (2014). He received the Hall Medal from the ICA (1999), was an Erskine Fellow at the University of Canterbury and a Hood fellow in Auckland. He is a member of the Royal Flemish Academy of Belgium for Science and the Arts.
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