A GENERAL METHOD TO OBTAIN THE SPECTRUM AND LOCAL SPECTRA OF A GRAPH FROM ITS REGULAR PARTITION

• Main Author: Fahri Rezi Ramadhan, M
• Format: Final Project
• Language: Indonesia
• Online Access: https://digilib.itb.ac.id/gdl/view/63595
• Institution: Institut Teknologi Bandung

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.