| Dewey Class |
511.6 |
| Title |
Distance-Regular Graphs ([EBook]) / by Andries E. Brouwer, Arjeh M. Cohen, Arnold Neumaier. |
| Author |
Brouwer, Andries Evert |
| Added Personal Name |
Cohen, Arjeh M. |
| Neumaier, Arnold |
| Other name(s) |
SpringerLink (Online service) |
| Publication |
Berlin, Heidelberg : Springer , 1989. |
| Physical Details |
XVII, 495 pages : online resource. |
| Series |
Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics 0071-1136 ; ; 18 |
| ISBN |
9783642743412 |
| Summary Note |
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.: |
| Contents note |
GRAPHS RELATED TO CODES -- 11.1 Completely regular codes -- Codes in distance-regular graphs -- Completely regular partitions and distance-regular quotient graphs -- Distance-regular graphs with regular abelian automorphism groups -- Completely regular codes in the Hamming scheme -- Completely regular codes in other distance-regular graphs -- 11.2 Graphs from the Kasami codes -- 11.3 Graphs from the Golay codes -- The coset graph of the extended ternary Golay code -- The coset graph of the ternary Golay code -- The coset graph of the truncated ternary Golay code -- The coset graph of the extended binary Golay code -- The coset graph of the binary Golay code -- The coset graph of the truncated binary Golay code -- The coset graph of the doubly truncated binary Golay code and the graph of the unitals in PG(2,4) -- Variations on the theme of coset graph - some antipodal covers -- 11.4 Graphs related to the Witt designs -- The Witt graph associated to M24 -- The truncated Witt graph associated to M23 -- The doubly truncated Witt graph associated to M22 -- The Ivanov-Ivanov-Faradjev graph -- Higman’s symmetric design -- The Leonard graph - M12.2 over PGL(2,11) -- The Hadamard association scheme -- Antipodal 2-covers of the Gewirtz graph -- The regular two-graph on 276 vertices and the McLaughlin graph -- 11.5 The van Lint-Schrijver partial geometry -- 12. GRAPHS RELATED TO CLASSICAL GEOMETRIES -- 12.1 The even orthogonal case; the Doro graph -- 12.2 The odd orthogonal case -- 12.3 The Coxeter graph for PSL(2,7) -- 12.4 The unitary case -- 12.5 Antipodal covers of complete graphs -- 12.6 Thin near octagons from Denniston’s complete arcs -- 12.7 Antipodal covers of complete graphs from pseudocyclic association schemes -- Cyclotomic schemes -- The Mathon and Hollmann schemes on 28 points, and conics in PG(2,q) -- The Hollmann scheme on 496 points -- 13. SPORADIC GRAPHS -- 13.1 Graphs related to the Hoffman - Singleton graph -- Sylvester’s double six graph -- 13.2 Commuting involutions graphs and Fischer spaces -- Five antipodal 3-covers -- The Foster graph for 3·Sym(6).2 and the hexacode -- The Conway-Smith graph for 3·Sym(7) -- The locally GQ(4,2) graph on 3×126 points -- The 3.O7,(3) graph on 3×378 points -- 13.3 The Perkel graph for L(2, 19) -- 13.4 The Biggs-Smith graph for L(2, 17) -- 13.5 The Livingstone graph for J1 -- 13.6 The near octagon associated with the Hall-Janko group -- 13.7 The Patterson graph for Suz -- 14. TABLES OF PARAMETERS FOR DISTANCE REGULAR GRAPHS -- A. APPEND -- A.1 Graphs -- A.2 Permutation groups -- A.3 Automorphisms -- A.4 Regular partitions, distribution diagrams and double . |
| System details note |
Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users) |
| Internet Site |
http://dx.doi.org/10.1007/978-3-642-74341-2 |
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