Zero-Symmetric Graphs (eBook)

Trivalent Graphical Regular Representations of Groups

H. S. M. Coxeter, Roberto Frucht, David L. Powers (Autoren)

eBook Download: PDF

2014 | 1. Auflage
180 Seiten
Elsevier Science (Verlag)
978-1-4832-6878-1 (ISBN)

Infos

Zero-Symmetric Graphs: Trivalent Graphical Regular Representations of Groups describes the zero-symmetric graphs with not more than 120 vertices.The graphs considered in this text are finite, connected, vertex-transitive and trivalent. This book is organized into three parts encompassing 25 chapters. The first part reviews the different classes of zero-symmetric graphs, according to the number of essentially different edges incident at each vertex, namely, the S, T, and Z classes. The remaining two parts discuss the theorem and characteristics of type 1Z and 3Z graphs. These parts explore Cayley graphs of specific groups, including the parameters of Cayley graphs of groups. This book will prove useful to mathematicians, computer scientists, and researchers.

Inhalt

Front Cover 1
Zero-Symmetric Graphs: Trivalent Graphical Regular Representations of Groups 4
Copyright Page 5
Table of Contents 8
Dedicated 6
Preface 10
PART I: GENERALITIES 12
CHAPTER 1. INTRODUCTION 14
CHAPTER 2. CAYLEY GRAPHS (IN GENERAL) 17
CHAPTER 3. TRIVALENT CAYLEY GRAPHS THE LCF AND FRUCHT NOTATIONS
CHAPTER 4. GENERAL REMARKS ON 0-SYMMETRIC GRAPHS 28
PART II: GRAPHS OF TYPE 1Z 32
CHAPTER 5. GENERAL REMARKS ON GRAPHS OF TYPE 1Z 34
CHAPTER 6. ZERO-SYMMETRIC GRAPHS OF GIRTH 38
CHAPTER 7. THE GROUPS Z(m,n,k) 41
CHAPTER 8. GRAPHS OF TYPE 1Z AND GIRTH 4 THAT ARE CAYLEY GRAPHS OF GROUPS Z(m,2,k) 46
CHAPTER 9. GRAPHS OF TYPE 1Z THAT ARE CAYLEY GRAPHS OF GROUPS Z(m,n,k), n > 2
CHAPTER 10. MORE O-SYMMETRIC CAYLEY GRAPHS OF Z(m,n,k) OBTAINED BY CHANGE OF GENERATORS 59
CHAPTER 11. THE JUXTAPOSITION PROCEDURE 62
CHAPTER 12. THE CAYLEY GRAPHS OF THE GROUPS F3, 2,-1 AND F4, 2, 1 THE EXTENDED LCF NOTATION
PART III: GRAPHS OF TYPE 3Z 72
CHAPTER 13. THE PARAMETERS OF CAYLEY GRAPHS OF GROUPS WITH THREE INVOLUTORY GENERATORS 74
CHAPTER 14. THE COMPANION GRAPHS OF CAYLEY GRAPHS OF GIRTH 82
CHAPTER 15. THE CAYLEY GRAPHS OF COXETER' S GROUPS Gp,q,r 85
CHAPTER 16. A PROCEDURE FOR OBTAINING BIPARTITE CAYLEY GRAPHS OF GIRTH 95
CHAPTER 17. THE CAYLEY GRAPHS OF THE GROUPS B(m,k) 101
CHAPTER 18. CAYLEY GRAPHS OF DIRECT PRODUCTS OF DIHEDRAL GROUPS 112
CHAPTER 19. MORE O-SYMMETRIC GRAPHS OF GIRTH 4 WITH 96 OR 120 VERTICES 118
CHAPTER 20. COMPANION GRAPHS OF HIGHER GIRTH 127
CHAPTER 21. PRELIMINARIES ON CAYLEY GRAPHS OF GIRTH 6 FOR DIHEDRAL AND RELATED GROUPS 131
CHAPTER 22. CAYLEY GRAPHS OF DIHEDRAL GROUPS WITH ONE REDUNDANT GENERATOR 137
CHAPTER 23. CAYLEY GRAPHS CF DIHEDRAL GROUPS WITH NO REDUNDANT GENERATOR 152
CHAPTER 24. CAYLEY GRAPHS OF GENERALIZED DIHEDRAL GROUPS 155
CHAPTER 25. YET ANOTHER O-SYMMETRIC GRAPH WITH 96 VERTICES 164
TABLES 166
BIBLIOGRAPHY 176
INDEX 180

Produkt-Details

• Erscheint lt. Verlag: 10.5.2014
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik
• Themenwelt: Technik
• ISBN-10: 1-4832-6878-0 / 1483268780
• ISBN-13: 978-1-4832-6878-1 / 9781483268781