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

Distance spectra of graphs: A survey

In 1971, Graham and Pollack established a relationship between the number of negative eigenvalues of the distance matrix and the addressing problem in data communication systems. They also proved that the determinant of the distance matrix of a tree is a function of the number of vertices only. Since then several mathematicians were interested in studying the spectral properties of the distance matrix of a connected graph. Computing the distance characteristic polynomial and its coefficients was the first research subject of interest. Thereafter, the eigenvalues attracted much more attention. In the present paper, we report on the results related to the distance matrix of a graph and its spectral properties.

Distance Spectra of Graphs: A Survey

An Introduction to the Theory of Graph Spectra: Introduction

Let G be a graph and denote by Q(G)=D(G)+A(G),L(G)=D(G)-A(G) the sum and the difference between the diagonal matrix of vertex degrees and the adjacency matrix of G,respectively. In this paper,some properties of the matrix Q(G)are studied. At the same time,anecessary and sufficient condition for the equality of the spectrum of Q(G) and L(G) is given.

Some properties of the spectrum of graphs

On graphs with at least three distance eigenvalues less than −1☆

Let G be a connected graph with distance matrix D(G), and let Tr(G) be the diagonal matrix of vertex transmissions of G. For any α∈[0,1], the Dα-matrix of G is defined as Dα(G)=αTr(G)+(1−α)D(G). In...

Huiqiu Lin

Papers

On graphs with at least three distance eigenvalues less than −1☆

On the Dα-spectra of graphs

The distance spectral radius of digraphs

Characterization of extremal graphs from distance signless Laplacian eigenvalues

Remoteness and distance eigenvalues of a graph