This book gives an elementary treatment of the basic material about graph spectra, both for ordinary, and Laplace and Seidel spectra. The text progresses systematically, by covering standard topics before presenting some new material on trees, strongly regular graphs, two-graphs, association schemes, p-ranks of configurations and similar topics. Exercises at the end of each chapter provide practice and vary from easy yet interesting applications of the treated theory, to little excursions into related topics. Tables, references at the end of the book, an author and subject index enrich the text. Spectra of Graphs is written for researchers, teachers and graduate students interested in graph spectra. The reader is assumed to be familiar with basic linear algebra and eigenvalues, although some more advanced topics in linear algebra, like the Perron-Frobenius theorem and eigenvalue interlacing are included.

Spectra of graphs

Consider a connected simple graph with vertex set X of diameter d. Define Ri X2 by (x, y) Ri whenever x and y have graph distance

Distance-Regular Graphs

Basic error estimates for elliptic problems

The aim of this paper is to describe the development of the method of fundamental solutions (MFS) and related methods over the last three decades. Several applications of MFS-type methods are presented. Techniques by which such methods are extended to certain classes of non-trivial problems and adapted for the solution of inhomogeneous problems are also outlined.

https://msvlab.hre.ntou.edu.tw/grades/meshless/MFS98.pdf

The method of fundamental solutions for elliptic boundary value problems

http://compalg.inf.elte.hu/~tony/Kutatas/BinPacking/Johnson-BinPacking-NP-Column-JAlg-2002.pdf

The NP-completeness column: An ongoing guide

The boundary conditions of an elliptic equation are approximated by using fundamental solutions with singularities located outside the region of interest as trial functions. By letting the singularities change their positions a highly adaptive though nonlinear approximation is achieved employing only a small number of trial functions. The method has been found to work well for problems with boundary data or boundaries of low continuity class. Of particular interest is the ease with which it can be applied to problems in three dimensions.

The Approximate Solution of Elliptic Boundary-Value Problems by Fundamental Solutions

A note on the graph isomorphism counting problem

Publisher Summary This chapter focuses on cyclic Steiner 2-Designs It surveys the literature relevant to cyclic Steiner S (2, k, u) systems A Steiner system S (t, k, u) is a collection of k-subsets of a u-set such that every t-subset of the u-set appears in exactly one of the k-subsets The chapter discusses the existence, enumeration, and the determination of isomorphism A brief historical overview and required definitions and notation are given

On Cyclic Steiner 2-Designs

2-( v , k , λ) Designs of Small Order

Boundary approximation techniques are described for solving homogeneous self-adjoint elliptic equations. Piecewise expansions into particular solutions are used which approximate both the boundary and interface conditions in a least squares sense. Convergence of such approximations is proved and error estimates are derived in a natural norm. Numerical experiments are reported for the singular Motz problem which yield extremely accurate solutions with only a modest computational effort.

Rudolf Mathon

Papers

The Approximate Solution of Elliptic Boundary-Value Problems by Fundamental Solutions

A note on the graph isomorphism counting problem

On Cyclic Steiner 2-Designs

2-( v , k , λ) Designs of Small Order

Boundary methods for solving elliptic problems with singularities and interfaces