Zero-Symmetric Graphs
Trivalent Graphical Regular Representations of Groups
Published on 10. May 2014
180 pages
978-1-4832-6878-1 (ISBN)
Description
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.
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01/1981
Academic Press
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Content
PrefacePart I Generalities 1 Introduction 2 Cayley Graphs (in General) 3 Trivalent Cayley Graphs; the LCF and Frucht Notations 4 General Remarks on 0-Symmetric GraphsPart 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 NotationPart 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 VerticesTablesBibliographyIndex
