![]()
内容推荐 在这本书中,作者研究在强正则图的参数上寻找合适的容许性条件的问题,并且添加了在这个领域内他们自己的贡献。本书给出了工作中必要的图论定义和主要结果,并且详细地介绍了强正则图的族。由于强正则图及其补图是一个具有两类的对称结合概形,作者也定义和介绍了这些组合结构。 作者简介 瓦斯科·马诺,2013年在波尔图大学以优异成绩获得应用数学博士学位。他在国际上广泛公开和发表的研究成果主要集中在谱图理论方面。 目录 Preface 1 An Introductory Background 1.1 The underlying main problem 1.2 The structure behind our problem: strongly regular graphs 1.2.1 General concepts of Graph Theory 1.2.2 Strongly regular graphs 1.2.3 Particular families of strongly regular graphs 1.2.4 Admissibility conditions 1.3 The main problem revisited 1.4 Going beyond strongly regular graphs: association schemes. 1.5 A similar algebraic structure with a different name: Euclidean Jordan algebras 1.5.1 Power-associative algebras 1.5.2 Jordan algebras 1.5.3 Euclidean Jordan algebras 1.5.4 A generalization of the Eigenvalues Interlacing The-orem to simple Euclidean Jordan algebras 2 Bringing Strongly Regular Graphs and Euclidean Jordan Alge-bras Together 2.1 An Euclidean Jordan algebra associated to the adjacency ma-trix of a strongly regular graph 2.2 A generalization of the Krein parameters 2.3 The generalized Krein admissibility conditions 2.4 A new upper bound for the Krein parameters 2.5 Some other admissibility conditions on the parameters of a strongly regular graph 2.5.1 Generalized binomial series 2.5.2 Function series 2.5.3 Alternating Hadamard series 2.6 Immediate consequences for association schemes and other results 2.7 Conclusions and remarks Bibliography Notation Index 编辑手记 |