Foundations of Economic Analysis

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

In order to store a graph or digraph in a computer, we need something other than the diagram or the formal definition. This something is the adjacency matrix, a matrix of O’s and l’s. The l’s correspond to the arcs of the digraph. Certain matrix operations will be seen to correspond to digraph concepts.

Graphs and Matrices

Combinatorial Matrix Theory

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Using Algebraic Geometry

Two graphs are said to be A-cospectral if they have the same adjacency spectrum. A graph G is said to be determined by its adjacency spectrum if there is no other non-isomorphic graph A-cospectral with G. A tree is called starlike if it has exactly one vertex of degree greater than 2. In this article, we prove that the line graphs of starlike trees with maximum degree at least 12 are determined by their adjacency spectra.

Spectral characterization of line graphs of starlike trees

Some block matrices with signed Drazin inverses

For a cycle C n , let C n ? 2K 1 be the graph obtained from C n by attaching two pendant edges to each vertex of C n . In this paper, we prove that C n ? 2K 1 is determined by its signless Laplacian spectrum when n ? 32, 64. We also show that C n ? 2K 1 is determined by its Laplacian spectrum.

Changjiang Bu

Papers

Spectral characterization of line graphs of starlike trees

Some block matrices with signed Drazin inverses

Spectral Characterizations of the Corona of a Cycle and Two Isolated Vertices

Resistance characterizations of equiarboreal graphs

A note on the multiplicities of graph eigenvalues