Distance-Regular Graphs

1. (i) Suppose K is a conjugacy class of Sn contained in An; then K is called split if K is a union of two conjugacy classes of An. Show that the number of split conjugacy classes contained in An is equal to the number of characters χ ∈ Irr(Sn) such that χAn is not irreducible. (Hint. Consider the vector space of class functions on An which are invariant under conjugation by the transposition (12).)

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Character Theory of Finite Groups

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 this window, all groups are assumed finite. Here we collect a number of results that play a significant role in the book (further material of an elementary nature that we sometimes take for granted is easily available in textbooks such as [H], [R] and [A]).

Finite Group Theory

An overview 1. Graph theory 2. Number theory 3. PSL2(q) 4. The graphs Xp,q Appendix A. 4-regular graphs with large girth Index Bibliography.

Elementary Number Theory, Group Theory, and Ramanujan Graphs: An Overview

Spectra of subdivision-vertex and subdivision-edge neighbourhood coronae

We survey some of the known results on eigenvalues of Cayley graphs and their applications, together with related results on eigenvalues of Cayley digraphs and generalizations of Cayley graphs.

Xiaogang Liu

Papers

Spectra of subdivision-vertex and subdivision-edge neighbourhood coronae

Eigenvalues of Cayley graphs

Quadratic unitary Cayley graphs of finite commutative rings

Laplacian state transfer in Q-graph

Computing the permanental polynomials of graphs