标题： 具有自环的可分设计图 显示英文标题

标题： Divisible design graphs with selfloops

摘要： 我们为可能包含自环的可分设计图（LDDG）发展了一个基本理论，并描述了两个无限族这样的图，其中一些成员也是没有自环的经典可分设计图（DDG）的例子。在所描述的理论结果中，包括谱的讨论，分类所有满足某些参数限制或最多有三个特征值的例子，对非正规和不连通例子结构的讨论，以及一种称为对偶西德尔切换的过程，该过程允许从其他例子构造新的LDDG的例子。 显示英文摘要

摘要： We develop a basic theory for divisible design graphs with possible selfloops (LDDG's), and describe two infinite families of such graphs, some members of which are also classical examples of divisible design graphs without loops (DDG's). Among the described theoretical results is a discussion of the spectrum, a classification of all examples satisfying certain parameter restrictions or having at most three eigenvalues, a discussion of the structure of the improper and the disconnected examples, and a procedure called dual Seidel switching which allows to construct new examples of LDDG's from others.