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Titlebook: Distance-Regular Graphs; Andries E. Brouwer,Arjeh M. Cohen,Arnold Neumaier Book 1989 Springer-Verlag Berlin Heidelberg 1989 Arithmetic.Lie

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书目名称Distance-Regular Graphs
编辑Andries E. Brouwer,Arjeh M. Cohen,Arnold Neumaier
视频video
丛书名称Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathemati
图书封面Titlebook: Distance-Regular Graphs;  Andries E. Brouwer,Arjeh M. Cohen,Arnold Neumaier Book 1989 Springer-Verlag Berlin Heidelberg 1989 Arithmetic.Lie
描述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.
出版日期Book 1989
关键词Arithmetic; Lie; geometry; mathematics; proof; symmetric relation; combinatorics
版次1
doihttps://doi.org/10.1007/978-3-642-74341-2
isbn_softcover978-3-642-74343-6
isbn_ebook978-3-642-74341-2Series ISSN 0071-1136 Series E-ISSN 2197-5655
issn_series 0071-1136
copyrightSpringer-Verlag Berlin Heidelberg 1989
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Theory of Distance-Regular Graphs,parts of the theory of distance-regular graphs independently of Chapter 2, we shall use concepts and results about association schemes for more specialized topics such as .-polynomial orderings (Chapter 8) and codes in graphs (Chapter 11). In §4.2 we look at various constructions that, given a dista
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Parameter Restrictions for Distance-Regular Graphs,y been mentioned in §4.1D.) Some of these restrictions are important tools in the theoretical investigation of the properties of distance-regular graphs, like the unimodality of the sequence (.). discussed in §5.1. (We already used this on several occasions.) Various bounds on the diameter in terms
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Graphs of Coxeter and Lie Type,In the later sections almost all known infinite families of distance-transitive graphs are described in this framework. The chapter ends with a determination of all distance-transitive graphs which naturally arise from a Tits system in a finite Chevalley group. Much more information on Tits systems,
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Graphs Related to Codes, .). We define the . Γ(.) . by taking as vertices the cosets of . in ., and joining two cosets when they have representatives that differ in one coordinate (i.e., have Hamming distance one). In some cases Γ(.) turns out to be distance-regular. In section 11.1 we study this phenomenon in a more gener
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Tables of Parameters for Distance Regular Graphs,regular graphs with diameter 4 on at most 4096 vertices, and for arbitrary distance-regular graphs of diameter at least 5 on at most 4096 vertices. In each category the parameter sets are ordered by . (not .). We only list intersectiòn arrays that pass all feasibility criteria known to us. We do not
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0071-1136 ting 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,
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