A GENERAL METHOD TO OBTAIN THE SPECTRUM AND LOCAL SPECTRA OF A GRAPH FROM ITS REGULAR PARTITION
Dalf´o and Fiol’s idea in their work entitled A General Method To Obtain The Spectrum and Local Spectra of a Graph from Its Regular Partition (2020) is studied in this final project. Van Dam and Haemers in Developments on Spectral Characterizations of Graphs (2009) describe various graphs that ar...
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| Format: | Final Project |
| Language: | Indonesia |
| Online Access: | https://digilib.itb.ac.id/gdl/view/63595 |
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| Institution: | Institut Teknologi Bandung |
| Language: | Indonesia |
| Summary: | Dalf´o and Fiol’s idea in their work entitled A General Method To Obtain The
Spectrum and Local Spectra of a Graph from Its Regular Partition (2020) is studied
in this final project. Van Dam and Haemers in Developments on Spectral Characterizations
of Graphs (2009) describe various graphs that are determined by their
spectrum which has led to a conjecture, that almost every graph is determined by
its spectrum. Part of the spectrum can be obtained from the adjacency matrix of
its quotient graph given by a regular partition. In this paper, the author examines a
method that gives the spectrum and the local spectra of a graph from the quotient
matrices of some of its regular partitions. The author also mentions several concepts
that construct the main result, including idempotent matrix, local multiplicity, local
spectra, crossed local multiplicity, and regular partition. The resulting method is
then applied to find the eigenvalues, local multiplicities, and spectrum of walkregular,
distance-regular, and distance-biregular graphs. |
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