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# Zero-Symmetric Graphs

## Trivalent Graphical Regular Representations of Groups

- 1st Edition - May 10, 2014
- Authors: H. S. M. Coxeter, Roberto Frucht, David L. Powers
- Language: English
- Paperback ISBN:9 7 8 - 1 - 4 8 3 2 - 3 7 7 3 - 2
- eBook ISBN:9 7 8 - 1 - 4 8 3 2 - 6 8 7 8 - 1

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… Read more

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Request a sales quoteZero-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.

Preface

Part I Generalities

1 Introduction

2 Cayley Graphs (in General)

3 Trivalent Cayley Graphs; the LCF and Frucht Notations

4 General Remarks on 0-Symmetric Graphs

Part II Graphs of Type 1Z

5 General Remarks on Graphs of Type 1Z

6 Zero-Symmetric Graphs of Girth 3

7 The Groups Z(m,n,k)

8 Graphs of Type 1Z and Girth 4 that are Cayley Graphs of Groups Z(m,2,fc)

9 Graphs of Type 1Z that are Cayley Graphs of Groups Z(m,n,k), n>2

10 More 0-Symmetric Cayley Graphs of Z(m,n,k) Obtained by Change of Generators

11 The Juxtaposition Procedure

12 The Cayley Graphs of the Groups F3,2,-1 and F4,2,1; the Extended LCF Notation

Part III Graphs of Type 3Z

13 The Parameters of Cayley Graphs of Groups with Three Involutory Generators

14 The Companion Graphs of Cayley Graphs of Girth 4

15 The Cayley Graphs of Coxeter's Groups Gp,q,r

16 A Procedure for Obtaining Bipartite Cayley Graphs of Girth 4

17 The Cayley Graphs of the Groups B(m,k)

18 Cayley Graphs of Direct Products of Dihedral Groups

19 More 0-Symmetric Graphs of Girth 4 with 96 or 120 Vertices

20 Companion Graphs of Higher Girth

21 Preliminaries on Cayley Graphs of Girth 6 for Dihedral and Related Groups

22 Cayley Graphs of Dihedral Groups with One Redundant Generator

23 Cayley Graphs of Dihedral Groups with no Redundant Generator

24 Cayley Graphs of Generalized Dihedral Groups

25 Yet Another 0-Symmetric Graph with 96 Vertices

Tables

Bibliography

Index

- No. of pages: 180
- Language: English
- Edition: 1
- Published: May 10, 2014
- Imprint: Academic Press
- Paperback ISBN: 9781483237732
- eBook ISBN: 9781483268781