报告人简介：Akihiro Munemasa教授在组合设计、编码和图的谱等领域做出了重要贡献。他的成就获得了同行的赞赏，例如，他是著名专业杂志 Algebraic Combinatorics 的主编以及 Graphs and Combinatorics的编委。
报告内容简介：A.J. Hoffman first gave a brief description of a theorem about the behavior of the smallest eigenvalues of graphs when some of
the vertices are replaced by cliques of increasing size. Hoffman claimed that this result would appear later in a joint paper with Ostrowski, but such a paper has never get published. Instead, Hoffman proved a slightly more general, signed graph version of the result, but the proof remained sketchy.
In this talk, we formulate this result as a theorem for general
Hermitian matrices purely in terms of matrices, so as to be applicable
for Hermitian adjacency matrices of digraphs. As an application, we show a signed analogue of Hoffman's theorem which states that a signed graph with smallest eigenvalue greater than -2 and large enough minimum degree is necessarily switching equivalent to a complete graph. Our proof is shorter than Hoffman's original which only deals with unsigned graphs, because we make use of the classification of integrally represented signed graphs with smallest eigenvalue greater than -2
This is joint work with Alexander Gavrilyuk, Yoshio Sano and Tetsuji Taniguchi.