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On trees with spectral radius three
2017年04月14日 来源： 浏览：303次
|讲座题目：On trees with spectral radius three|
主讲人 ：Prof. Jack Koolen
Jack Koolen，中国科学技术大学数学科学学院教授，学术期刊Graphs and Combinatorics执行编辑。在国际期刊上发表了多篇学术论文，包括《Journal of Combinatorial Theory》、《Inventiones Mathematicae》、《Advances in Mathematics》。
Abstract: Smith, in the 1970''s, classified the connected graphs with spectral radius two. They are intimately related to the irreducible root lattices. In this talk I will discuss trees with spectral radius three. It is much harder to classify these trees as there are so many more examples. We try to obtain some structure theory for these trees. To discuss our main result we need to introduce some notation. We say that a graph G is integrally representable with norm t, if there exists an integral matrix N such that the adjacency matrix A of G can be written as A +tI = NN^T. In this talk we will classify the trees that are integrally representable with norm 3. We will also discuss some future work. This is joint work with Masood Ur Rehman and Qianqian Yang.