E-Book, Englisch, 180 Seiten, Web PDF
Coxeter / Frucht / Powers Zero-Symmetric Graphs
1. Auflage 2014
ISBN: 978-1-4832-6878-1
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark
Trivalent Graphical Regular Representations of Groups
E-Book, Englisch, 180 Seiten, Web PDF
ISBN: 978-1-4832-6878-1
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark
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.
Autoren/Hrsg.
Weitere Infos & Material
1;Front Cover;1
2;Zero-Symmetric Graphs: Trivalent Graphical Regular Representations of Groups;4
3;Copyright Page;5
4;Table of Contents;8
5;Dedicated;6
6;Preface;10
7;PART I: GENERALITIES;12
7.1;CHAPTER 1. INTRODUCTION;14
7.2;CHAPTER 2. CAYLEY GRAPHS (IN GENERAL);17
7.3;CHAPTER 3. TRIVALENT CAYLEY GRAPHS; THE LCF AND FRUCHT NOTATIONS;20
7.4;CHAPTER 4. GENERAL REMARKS ON 0-SYMMETRIC GRAPHS;28
8;PART II: GRAPHS OF TYPE 1Z;32
8.1;CHAPTER 5. GENERAL REMARKS ON GRAPHS OF TYPE 1Z;34
8.2;CHAPTER 6. ZERO-SYMMETRIC GRAPHS OF GIRTH;38
8.3;CHAPTER 7. THE GROUPS Z(m,n,k);41
8.4;CHAPTER 8. GRAPHS OF TYPE 1Z AND GIRTH 4 THAT ARE CAYLEY GRAPHS OF GROUPS Z(m,2,k);46
8.5;CHAPTER 9. GRAPHS OF TYPE 1Z THAT ARE CAYLEY GRAPHS OF GROUPS Z(m,n,k), n > 2;52
8.6;CHAPTER 10. MORE O-SYMMETRIC CAYLEY GRAPHS OF Z(m,n,k) OBTAINED BY CHANGE OF GENERATORS;59
8.7;CHAPTER 11. THE JUXTAPOSITION PROCEDURE;62
8.8;CHAPTER 12. THE CAYLEY GRAPHS OF THE GROUPS F3, 2,-1 AND F4, 2, 1; THE EXTENDED LCF NOTATION;65
9;PART III: GRAPHS OF TYPE 3Z;72
9.1;CHAPTER 13. THE PARAMETERS OF CAYLEY GRAPHS OF GROUPS WITH THREE INVOLUTORY GENERATORS;74
9.2;CHAPTER 14. THE COMPANION GRAPHS OF CAYLEY GRAPHS OF GIRTH;82
9.3;CHAPTER 15. THE CAYLEY GRAPHS OF COXETER' S GROUPS Gp,q,r;85
9.4;CHAPTER 16. A PROCEDURE FOR OBTAINING BIPARTITE CAYLEY GRAPHS OF GIRTH;95
9.5;CHAPTER 17. THE CAYLEY GRAPHS OF THE GROUPS B(m,k);101
9.6;CHAPTER 18. CAYLEY GRAPHS OF DIRECT PRODUCTS OF DIHEDRAL GROUPS;112
9.7;CHAPTER 19. MORE O-SYMMETRIC GRAPHS OF GIRTH 4 WITH 96 OR 120 VERTICES;118
9.8;CHAPTER 20. COMPANION GRAPHS OF HIGHER GIRTH;127
9.9;CHAPTER 21. PRELIMINARIES ON CAYLEY GRAPHS OF GIRTH 6 FOR DIHEDRAL AND RELATED GROUPS;131
9.10;CHAPTER 22. CAYLEY GRAPHS OF DIHEDRAL GROUPS WITH ONE REDUNDANT GENERATOR;137
9.11;CHAPTER 23. CAYLEY GRAPHS CF DIHEDRAL GROUPS WITH NO REDUNDANT GENERATOR;152
9.12;CHAPTER 24. CAYLEY GRAPHS OF GENERALIZED DIHEDRAL GROUPS;155
9.13;CHAPTER 25. YET ANOTHER O-SYMMETRIC GRAPH WITH 96 VERTICES;164
10;TABLES;166
11;BIBLIOGRAPHY;176
12;INDEX;180
