Graph operations and Techniques to compute the Adjacency Graph spectra

Banerjee, Agnivo (2023) Graph operations and Techniques to compute the Adjacency Graph spectra. Masters thesis, Indian Institute of Science Education and Research Kolkata.

Text (MS dissertation of Agnivo Banerjee (17MS093)) Thesis_17MS093.pdf - Submitted Version Restricted to Repository staff only Download (1MB)

Abstract

Spectral Graph theory is about studying spectra of different graphs. Throughout this work,we are mainly interested in Adjacency spectra of Graphs. In the introductory Chapter,we go through the pre-requisites, the preliminaries of Spectral Graph theory.In Chapter-2,we state a condition which helps us finding eigenvalues and eigenvectors of graphs,and we work out some examples, as well learning techniques like localized eigenvectors. In the final chapter, we learn several graph operations,that is,creating new larger graphs out of smaller ones.Here we study some techniques other than localized eiegenvectors, which are essentially Graph Homomorphisms,useful to recover the whole spectrum of the new graphs with the use of that of the smaller ones.Such techniques include equitable partitions and 2-edge covering.

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