Modern Graph Theory

Preface 1. Introduction 2. Graph operations and modifications 3. Spectrum and structure 4. Characterizations by spectra 5. Structure and one eigenvalue 6. Spectral techniques 7. Laplacians 8. Additional topics 9. Applications Appendix Bibliography Index of symbols Index.

An Introduction to the Theory of Graph Spectra: Spectral techniques

An Introduction to the Theory of Graph Spectra: Introduction

On the spectrum of the normalized Laplacian of iterated triangulations of graphs

Spectral graph theory looks at the interplay between the structure of a graph and the eigenvalues of a matrix associated with the graph. Many interesting graphs have rich structure which can help in determining the eigenvalues associated with a particular graph matrix. This survey looks at some common techniques in working with and determining the eigenvalues associated with the normalized Laplacian matrix, in addition to some algebraic applications of these eigenvalues.

Algebraic aspects of the normalized Laplacian

Effect on normalized graph Laplacian spectrum by motif attachment and duplication

A complex unit gain graph is a simple graph in which each orientation of an edge is given a complex number with modulus 1 and its inverse is assigned to the opposite orientation of the edge. In thi...

On the adjacency matrix of a complex unit gain graph

On the normalized spectrum of threshold graphs

Funding: CSIR, India (Grant No-09/983(0037)/2019-EMR-I), SERB, India through Core Research Grant (File Number-CRG/2020/000447).

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Ranjit Mehatari

Papers

Effect on normalized graph Laplacian spectrum by motif attachment and duplication

On the adjacency matrix of a complex unit gain graph

On the normalized spectrum of threshold graphs

Forbidden subgraphs of power graphs

An eigenvalue localization theorem for stochastic matrices and its application to Randić matrices