| Budget Amount *help |
¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000)
Fiscal Year 2017: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2016: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2015: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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| 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.
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