四川师范大学
四川师范大学 Sichuan Normal University
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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
讲座时间:2017-4-17 10:00:00
讲座地点:狮子山校区6教811
主办单位:数学与软件科学学院
主讲人 :Prof. Jack Koolen
主讲人简介:
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.