The series is devoted to the publication of monographs and high-level textbooks in mathematics, mathematical methods and their applications. Apart from covering important areas of current interest, a major aim is to make topics of an interdisciplinary nature accessible to the non-specialist.
The works in this series are addressed to advanced students and researchers in mathematics and theoretical physics. In addition, it can serve as a guide for lectures and seminars on a graduate level.
The series de Gruyter Studies in Mathematics was founded ca. 35 years ago by the late Professor Heinz Bauer and Professor Peter Gabriel with the aim to establish a series of monographs and textbooks of high standard, written by scholars with an international reputation presenting current fields of research in pure and applied mathematics.
While the editorial board of the Studies has changed with the years, the aspirations of the Studies are unchanged. In times of rapid growth of mathematical knowledge carefully written monographs and textbooks written by experts are needed more than ever, not least to pave the way for the next generation of mathematicians. In this sense the editorial board and the publisher of the Studies are devoted to continue the Studies as a service to the mathematical community.
Author(s): Ulrich Knauer, Kolja Knauer
Series: De Gruyter Studies in Mathematics
Edition: 2nd Rev. and Ext. ed. edition
Publisher: De Gruyter
Year: 2019
Language: English
Pages: 349
Cover......Page 1
De Gruyter Studies in Mathematics, Volume 41
......Page 3
Algebraic Graph Theory: Morphisms, Monoids and Matrices
......Page 5
© 2019......Page 6
Preface......Page 7
Preface for the second edition......Page 13
Contents
......Page 15
1 Directed and undirected graphs......Page 21
2 Graphs and matrices......Page 49
3 Categories and functors......Page 69
4 Binary graph operations......Page 85
5 Line graph and other unary graph operations......Page 111
6 Graphs and vector spaces......Page 125
7 Graphs, groups, and monoids......Page 157
8 The characteristic polynomial of graphs......Page 183
9 Graphs and semigroups......Page 203
10 Compositions, unretractivities, and monoids......Page 229
11 Cayley graphs of semigroups......Page 245
12 Vertex transitive Cayley graphs......Page 267
13 Embeddings of Cayley graphs—genus of
semigroups......Page 281
List of cited papers, theses etc.......Page 323
List of books......Page 327
Index......Page 339
Index of symbols......Page 347