Zero-Symmetric Graphs

Zero-Symmetric Graphs

Trivalent Graphical Regular Representations of Groups

1st Edition - January 28, 1981

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  • Authors: H. S. M. Coxeter, Roberto Frucht, David L. Powers
  • eBook ISBN: 9781483268781

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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.

Table of Contents

  • 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




Product details

  • No. of pages: 180
  • Language: English
  • Copyright: © Academic Press 1981
  • Published: January 28, 1981
  • Imprint: Academic Press
  • eBook ISBN: 9781483268781

About the Authors

H. S. M. Coxeter

Roberto Frucht

David L. Powers

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