Selected topics from algebraic graph theory. Lecture notes (Q2810317)

This is a useful resource for someone studying algebraic graph theory, or as notes for a course on that topic. A course based on these notes should be aimed at least at the level of an advanced undergraduate student. The first author has offered many courses in algebraic graph theory; the second author took one of these courses as a postdoctoral fellow with minimal background in this field but interest in learning enough quickly to undertake research. The two collaborated to publish their combined notes. Exercises and sample take-home exams are included without solutions.NEWLINENEWLINEThe authors suggest that this course requires undergraduate background in both algebra and graph theory. From reading the book, a lot of background in the areas of linear algebra, permutation groups, and graph theory is expected; I would recommend at least a strong undergraduate course on each of these topics. There is an introductory chapter on combinatorial preliminaries that is particularly brief in its description of material, but some of these topics are also returned to later in the book in more detail. Sometimes concepts that I would not expect from any undergraduate background (such as the root systems \(E_6\), \(E_7\), and \(E_8\)) arise without explanation, but these concepts can be emphasized or glossed over according to the interest and background of the reader or students.NEWLINENEWLINEThe book is written as notes, often in point form as they would be written in class. A careful reader will observe occasions when the phrasing used might hint that English is not the authors' first language, but overall the English is excellent and the use of language does not interfere with comprehension.NEWLINENEWLINEThere is an excellent list of additional references at the end of the book, in addition to the bibliography. A reader who wants to understand the concepts in depth would be well-advised to have many of these references on hand or available to fill in details, as some proofs and explanations are made only by reference.NEWLINENEWLINEThe authors mention computation in the introduction, and recommend its use in some exercises, but do not explicitly invoke any particular computation methods, so the reader is free to make use of technology (or not) as they see fit.NEWLINENEWLINETopics covered include linear algebra and graph theory; permutation groups (with a focus on group actions; graphs appear in this context only as a type of relation); coherent configurations; association schemes; strongly-regular graphs; and spectra of graphs.