Research on Discrete Structure and Algorithms by using Spectral Graph Theory

2017 Fiscal Year Final Research Report

• Project/Area Number: 15K20885
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Foundations of mathematics/Applied mathematics; Theory of informatics
• Research Institution: University of Tsukuba
• Principal Investigator: Sano Yoshio 筑波大学, システム情報系, 准教授 (20650261)
• Project Period (FY): 2015-04-01 – 2018-03-31
• Keywords: グラフ理論 / アルゴリズム / グラフ固有値 / 離散構造 / マトロイド / マッチング / メカニズムデザイン

Outline of Final Research Achievements

We have obtained the following results: (i) We studied the eigenvalues and the characteristic polynomials of the line graphs of generalized Bethe trees, and we solved an open problem posed by Cvetkovic and Stevanovic in 2003 by using our results. (ii) We gave a complete classification of edge-signed graphs whose signed adjacency matrices have smallest eigenvalue greater than -2, which is a generalization of a classical result on the classification of graphs whose adjacency matrices have smallest eigenvalue greater than -2 by Doob and Cvetkovic in 1980. As a result, we solved a conjecture by Hoffman given in 1977. Also we obtained new results on Hoffman graphs by using our results.

Free Research Field

離散数学