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08-26【Willem Haemers】管楼1218吴文俊数学重点实验室组合图论系列讲座之142

澳门新葡新京:系统管理员发布时间:2019-08-12浏览次数:10


Title:Which graph properties are characterized by the spectrum?

Speaker:Willem Haemers(Tilburg University of Economics and Management, Holland)

Time:2019年8月26号     下午:4:00-5:00

Room:东区管理科研楼1218

Abstract:Spectral graph theory deals with the relation between the structure of a graph and the eigenvalues (spectrum) of an associated matrix, such as the adjacency matrix A and the Laplacian matrix L. Many results in spectral graph theory give necessary condition for certain graph properties in terms of the spectrum of A or L. Typical examples are spectral bounds for characteristic numbers of a graph, such as the independence number, the chromatic number, and the isoperimetric number. Another type of relations are characterization. These are conditions in terms of the spectrum of A or L, which arc necessary and sufficient for certain graph properties. Two famous examples are: (i) a graph is bipartite if and only if the spectrum of A is invariant under multiplication by 1, and(ii) the number of connected components of a graph is equal to the multiplicity of the eigenvalue 0 of L. In this talk we will survey graph properties that admit such a special characterization.
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