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
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)
>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