Tymoshkevych L. Direct and inverse spectral problems for weighted finite graphs and countable Coxeter graphs.

Українська версія

Thesis for the degree of Candidate of Sciences (CSc)

State registration number

0415U003832

Thesis Registration Form

0415U003832.pdf

Applicant for

Specialization

  • 01.01.06 - Алгебра і теорія чисел

08-06-2015

Specialized Academic Board

Д 26.001.18

Taras Shevchenko National University of Kyiv

Essay

Inverse spectral problems are studied, namely, how to reconstruct graph edge weights from the spectral data of graph and its subgraphs. For Dynkin graphs it is found out, what number of subgraph spectra is sufficient to determine the edge weights in a unique manner. It is proved that for a tree this number does not exceed that of pendant vertices, and this bound is precise for the star graph. The thesis contains results on the graph classification with respect to the index value, namely, Smith-like therem for countable Coxeter graphs is proved.

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Files

aref.pdf

dis.pdf

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