Strongly Regular Graphs

Andries E. Brouwer · H. Van Maldeghem

ม.ค. 2022 · Encyclopedia of Mathematics and its Applications หนังสือเล่มที่ 182 · Cambridge University Press

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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.

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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.